Yes if you blow air (especially heated air) over various oil-based finishes they will dry faster.
Is there any reason not to?
Hairdryer first: you're unlikely to cause a problem unless you get really close (nozzle only an inch or so/couple of cm from the wood surface) and it fits the bill theoretically, but you'd die of boredom before you see any benefit. You could in theory set up a hairdryer on a stand blowing over the piece and leaving it for a couple of hours but they're not made for that kind of sustained use and I bet you'd burn out the average modern hairdryer in short order.
Heat gun: this can easily cause a problem. With the typical temperatures these can generate you could accidentally heat the piece past the point where water will start to be released from the surface wood fibres, and it will literally start to bubble through the finish. I've accidentally done this using a hairdryer (being impatient and speed-curing epoxy fills on finished tool handles) so no question it would be even easier with a heat gun.
Where you do see the basic idea applied successfully is using fan heaters. Typically they'd be set up a few feet/a metre or so from the piece and blowing warmed air over it. In cooler weather, particularly if it's not dry, this can make a big difference in the drying of some finishes so it can be well worth experimenting with if you have an unheated shop or working space. Note though that there is quite some risk of the currents of air disturbing sanding dust from some hidden corner and making it airborne, and you can bet it will unerringly find its way to the finished surface.