The latter is a legitimate concern and it's why I believe it is most common for a finished surface on reclaimed wood to be taken off by other means. These days that appears to be most frequently with either with a belt sander2 or a wide-belt sander. Finish building up on the blades is a real issue, just as it isresin buildup from resins inresinous wood itselfspecies is, and while to be fair it is pretty easily removed to be fair I think itthis still falls firmly into the category of prevention is better than cure category.
A roughing plane of some sort — a true scrub plane or a similar-sized plane converted to scrub duties, or a traditional roughing jack or fore plane — can make short work of taking off even veryvery thick finish likesuch as many layers of paint assince their curved cutting edges scoop under the surface.
Because of this scooping action the plane irons can stay sharp longer than you'd expect even when the surface is dirty because they interact minimally with the finish and are mostly cutting wood. And even when (not if!) a bitspeck of embedded grit nicks the iron it's not a big deal and you can usually ignore it because the plane is not producing the final surface. These irons also don't have to be super super sharp like most people aim for on a smoothing plane, so when it comes time to hone it can be very quick — 30 seconds to a couple of minutes at most (I aim to get my irons back in the plane in under three minutes).
If you need to retain the wood surface under the finish
Have to mention this as occasionally you do want to retain the woodoriginal surface on older wood, under a clear finish especially but even under paint if the wood is old enough. The colour of the aged or 'patinated' surface has taken decades or longer to get to this colourdevelop and taking off even a thinnish layer of wood from the surface of boards can get below this, all (all the way to fresh wood in some cases,) removing some or all of the very thing you wanted the reclaimed wood for in the first place.
One last option, flip the boards over
The underside of boards often have no finish on them and for some projects you could ignore the finish on the other side and use the boards almost as-is. YouIn addition to the saving in work, you retain as much thickness as possible this way.
4 Something to be aware of removing old paint and varnish that may contain lead or other heavy metals, unless your dust collection is practically 100% effectiveefficient.