Hey now, 4HP (peak obviously) doesn't have to be that bad.
I mean think about some of the power tools around that are pushing 2+ HP. My router is 2.25HP and spins past 20k. Shop Vacs are beyond 3HP and spin at a decent speed. A good electric chainsaw can be made, but the real question is the Worx unit for less than $100 it...
Honestly, I've never ran an electric one. But for $100 I doubt it'd do much more than light pruning and small limbs. Pull an 18" chain/bar...yeah probably not unless those rakers are set really high. Now a 14" bar/chain with the thinnest kerf chain it might possibly work alright.
Besides HP rating in electric units is really over rated. Electric motors really shine at torque. Depending on motor design and complexity you could get a really compact electric unit spinning an 18" bar/chain setup just as easily as any 50CC saw...only problem would be the fact it'd cost you as much if not more than a 50CC saw.
Look at the new brushless motor drills, lighter, smaller, and better on battery life. The trade off is more electronics to break.