You can use a countertop blender, but you're limited on the size of the batch you can make. But it works -- there's a gal in south-east Minnesota who has a thriving soap making business and uses countertop blenders to make all her soap.
On the other hand, I have to say if a person is stick blending their soap batter long enough to overheat or burn out the motor, they're using a stick blender incorrectly. So I'm not sure your thought to use a countertop blender is based on a valid issue. Learn to use a SB with more finesse, and the problem becomes a non-problem.
For NaOH soap, I typically stick blend for a total of maybe 30 seconds, often less, in bursts of a few seconds at a time. I use a stick blender more with KOH soap, but it's also in relatively short bursts with some minutes in between uses. So the motor never overheats.