Can a variac be used to maintain constant voltage?

So, if an ordinary variac does not maintain voltage at its fixed setting, what is the purpose of using such a variac, i.e. is it simply to revive an old amp from storage for instance by slowly increasing the voltage to nominal levels?

My own reason for having this variac in the first place is that prior to the Threshold, I was using a pair of vintage vacuum tube monoblocks running 8 el34's per side: when turned on the amps would spike to the maximum level as gauged by their ammeters and then settle back down to the nominal 6 amp running rate: so, rather than having to deal with this initial surge and its potential negative impact, I bought the variac to slowly bring up the amps to running voltage. The variac is selling for a few dollars short of $600.00 now and I do not if its worth keeping this expensive piece for any valuable audio uses -- i.e. reduction of high frequency noise as Almarg mentions above -- or sell it off to someone with a more suitable application. I still find it amazing that the variac is showing a consistent 120 volts as set by my original dial setting. I had a PS Audio Power Plant Premier at one time and the incoming voltage showed as high as 125 volts sometimes. So it makes me wonder if the variac is not in fact more useful in my current Threshold application as might otherwise seem.

On a related point what is the difference between a variac and an autotransformer (which is what I have)? Thanks.

Thanks all for your informative input. I guess a variac is simply not suitable for my purposes so I am selling it.