Electrolysis won't work - you will electrolyse water, not H+ from the acid.
As for equivalents.
Imagine you have a sample of acid of known mass.
Equivalent is formally defined as amount of substance that reacts with 1 mole of electrons. This definition is a little bit to narrow IMHO. Druing neutralization there are no electrons involved (well, they are, but it is hardly reaction WITH electrons). But - if you will react H+ with Zn - you will see that exactly 1 mole of H+ reacts with 1 mole of electrons. In the case of acids 1 equivalent is 1 acidic proton.
When you titrate it with base, you know how many acid equivalents have been neutralized. You don't know how many moles of acid it was. This gives you information about mass of equivalent, not about molar mass.
There are other methods of determining molar mass - freezing point depression, boiling point depression, volume of gas (PV=nRT) to name a few. Unfortunately, they are not easy to use in the case of sulfuric acid, but we are talking about general approach.
So, what you can do is to determine mass of equivalent by titration, then molar mass by other means. If they are identical - you know there is one acidic proton per molecule. If they differ - molar mass should be a multiply of equivalent, molar/equivalent mass ratio gives you number of protons.