Yes and no.  It improves the CRI quite dramatically, but also reduces life.  Lithium iodide is far more corrosive towards quartz than sodium iodide, due to its smaller atoms which more easily penetrate and attack the silica structure.

The above comments are correct, but it should also be noted that the sodium does not actually react with the aluminium oxide arc tube to any great extent.  Wikipedia is completely wrong in this respect.  The sodium does react slightly with some dopants in the crystalline structure of the alumina, notably the magnesium oxide and calcium oxide components which are present at the grain boundaries.  This gradually makes the arc tube wall more porous during life.  Sodium atoms are then able to diffuse along the grain boundaries and leak into the outer bulb, where they react with the glass bulb and cause additional darkening which reduces luminous flux and traps more heat inside the lamp, further exacerbating the voltage rise caused by arc tube blackening.

There is also extensive reaction between sodium and the glassy frit-seals at the arc tube ends, and with the barium tungstate emitter coating of the electrodes.  In that case the sodium does not leave the arc tube but becomes chemically bound with those components.

As Dez mentioned, the primary ageing mechanism of standard HPS lamps is the changing amalgam ratio.  HPS lamps reach peak efficiency and luminous flux when the delta-lambda distance between the two spectral peaks either side of the sodium resonance radiation is about 120 Angstroms.  But as the sodium-mercury ratio increases and the arc tube temperature rises due to blackening, the red-wing of the sodium spectrum is broadened and the d-line is also broadened.  More red and infrared radiation is produced by the plasma, so the luminous flux must decrease.

Note that these failure mechanisms are entirely different in the higher performance Unsaturated Vapour HPS lamps.  These are actually characterised by a falling lamp voltage during life, since there is no excess of sodium and the whole dose is vaporised.  Therefore no longer so dependent on the cold spot temperature and its changes during life as a result of blackening.  USV lamps are only feasible when the sodium-sinks are reduced or eliminated.  So the alumina arc tubes tend to be doped with zirconium or erbium oxides in addition to magnesium oxide, and with reduced calcium oxide impurity, which reduces sodium reactions at the grain boundaries and hence the rate of sodium loss.  Of far more importance though is the change of electrode emitter material, usually one of the biggest sodium sinks.  The traditional barium tungstate emitter is changed to something less reactive - in the case of the Sylvania lamps that was BSY2, barium strontium yttrate combined with a special sintering procedure.  Some companies also used more resistant frit sealing glasses.  Incidentally just before the USV lamps fail and the last of their sodium is consumed, there is a sudden rapid rise in voltage back up to something close to the original level.  This characteristic ensures that there is no end-of-life cycling.  Lamps turn completely blue when the sodium is gone, and continue to burn as a pure mercury discharge.  But then of course the plasma temperature increases, and since the ceramic arc tube is not chemically stable enough to withstand a pure mercury arc (sodium or metal halides are required to protect it), the ceramic eventually disintegrates and leads to complete lamp failure. 

If you want to learn more about this I can highly reccomend the book of one of my former colleagues, Sjef de Groot at Philips Eindhoven, who wrote "The High Pressure Sodium Lamp".  There was a copy going cheaply on Ebay for a long time that seems not to have sold but now I cannot find it.  That book is rather old and does not cover the newer developments like the USV, deluxe/white, retrofit, high xenon pressure, mercury-free lamps etc.  The subject was brought just about fully up to date in a comprehensive IEEE paper written in 1993 by my old boss at Sylvania, Rudy Geens, and our American colleague Elliot Wyner.  See https://digital-library.theiet.org/doi/abs/10.1049/ip-a-3.1993.0070  I can send a copy if you do not manage to find it via the usual scientific literature sources.

I've partially corrected the thing with the EOL cycling in Wikipedia. If it is still not good enough, I would recommends you to correct the thing.

I tried both lamps in one of my fixtures. 
F18T8 0.32A 52% PF
F17T8 0.28A 61% PF

and another which underdrives lamps.
F18T8 0.24A 51% PF
F17T8 0.20A 63% PF

The only issue I've encountered is difficulty starting in the second fixture.  The current is too low to preheat the cathodes adequately, though it worked better when the lamp was new.  I'm actually still using that fixture with the F17, but I've fitted it with a Pulsetarter.  I've never had stability issues once lit.  The F17 never shimmers or drops out.

@NeXe Lights, my hunch is an F17 will be fine, but it might wear out quicker especially if frequently switched.

I cannot seem to find these for less than $4 per tube for a case of them. So, I thought I'd ask for some help.

I’ve subbed

Quick question: now I'm looking to make videos for incandescents and CFLs. I found the sweet spot for tubes, 3-4 lamps. But what would it be for incandescent lamps and CFLs?How many bulbs should I include in one video?

Won't F17 arc voltage be a bit too high to be stable with a choke on 120V +-10% ?

@RRK, @James?

Is there any advantage for the lithium impurity in white QMH lamps?

Doesn't the higher arc voltage of the F17 cause the ballast current to drop?
So the ballast could deliver the 0.27A for the F17 lamp and something around 0.33A for the F18T8. Assuming about 15V drop on the ballast wire resistance, we are talking abou roughly 97V vs 81V drop (F18 vs F17) across the inductive part, plus a bit larger degree of saturation for the core.
And the 0.33A is not that far from the 0.365 rated current for the F18.
And because of the thing is not governed by EU standards (banning all ballast not driving the lamp at its full rated light output), it could be the way the ballast is designed to serve both (and even some more) lamp types.