I got an engine/cabin heater installed into my car right before winter, which was great for driving comfort this winter. One of its "side-effect" features is that it charges and keeps your battery at 14.1 volts while it's connected.
Does this have any effect on the battery's lifespan or is it just going to hide issues with a failing battery? Does it really influence anything at all?
As long as it is not overcharging your battery, it will increase the useful life of the battery. The reason behind this is, as a battery sits, it loses power. Some of the electrolysis which goes on to make a battery work, also breaks down the battery. During this period, the battery goes through a sulfating period, where sulfur crystals grow on the lead plates. This only happens during discharge. The better charge which is on the battery, the less sulfation occurs. As your charger is keeping the battery topped off, it is also slowing the sulfation condition, which prolongs the life. Please realize a battery is not going to last forever, but a well maintained battery is going to last much longer than a battery which just sits. Maintaining the battery in this sense helps keep the battery in good shape, which is never a bad thing.
