It could be, but it is not a certainty.
Or let me put it another way. All of these model of Macs need new capacitors. But, that may not be the cause or the only cause of your problem.
My IIci needed new caps back in the mid-90s. But, not only did the caps give out on me, the goo from the caps ate through a via (pass through hole in circuit board) on the logic board which connected a front layer trace to a back layer trace. The damage was not at all obvious and it required examination with a magnifier and then testing with a multimeter to identify. Once I found it, it was easy enough to bypass with a little bit of wire.
But I would never have known to look, if someone had not posted about this kind of problem in the news groups back then.
I think that our user, Dennis Nedry, had some traces to his ROMs damaged by capacitor leakage, but I may be misremembering.
So, replacing the caps has a good chance of fixing the problem, but it might not.