Hey pica, thanks for the promo!
Anyway, household water softeners replace hardness minerals (like calcium carbonate) with salt (i.e., sodium chloride). This is one reason baby food should never be made up with softened water, and why the drinking water tap is usually left taking water from the direct water supply and not the softened water supply. Hence, softened water done this way (known as ion exchange) isn't the same thing as softened water that's come through a reverse osmosis system (which has no minerals of any kind in it).
Personally, I wouldn't use softened water in an aquarium, though many people have, and had no problems. Truly, the only sure way to know is to compare the salinity, hardness, and pH of the well water and the softened water, and see what they're like. If one is obviously better than the other, act accordingly. If you don't have all these test kits to hand, your local aquarium shop may do the tests for you (it's quite common for British aquarium shops at least to do water tests for £1 per go).
Convicts do perfectly well (in fact rather like) hard, alkaline water and should adapt to the well water easily. On the flip side, they don't mind a little salt, either, so if you wanted to mix well water with softened water 50:50, that might actually work quite nicely. I wouldn't keep them in soft water though, as they like at least moderate hardness and a neutral to alkaline pH.
One caveat to well water in aquaria is this: while usually very pure and clean, I have heard of instances where it was polluted with ammonium and nitrates from agricultrual run-off. If it's safe to drink, then it should be fine, but I'd check anyway.
Cheers, Neale