Can slimline lamps suffer from the affects of cold cathode discharge?
Yes, the same as other fluorescents.
The heat to warm up the cathodes does not come from the filament supply (well, except dimmable ballasts on a very reduced power setting), but from the ions bombarding it (at lower speed, so way less damaging, but still bombarding; that is the main mechanism how cathodes age - this bombardment does slowly wear the surface off, the low spead just means it is so slow the cathode endures the 20k hours of rated life).
Where the slimlines (and all lamps started without cathode preheat) do suffer is starting - because there is no means to heat up the cathodes before the arc is established, the arc is always burning for some time on cold cathodes before the ion bombardment delivers enough heat to warm the material up. It usually takes about a second or so.
By the way this is the main mechanism, why fluorescents do not like frequent starting in general. Although many ballast topologies do provide heating power to cathodes, usually it is just enough to allow easy arc strike, but still not enough to avoid the accelerated cold cathode wear.
To really avoid it, the preheating will need some seconds (too high power may reach the temperature sooner, but it may overheat the thinner parts of the filaments and damage them that way), what means quite noticeable delay between the switch turn ON and actually getting the light (it is how programmed start ballasts work and how they achieve the high lamp cycle life).
And dont get misled by the few second delay with a glowbottle starter preheat: There the few second delay is not preheating the lamps, but just heating up the starters to do something. The lamp preheating there is barely half second or so, so still not enough for a wear less starting.
