I think tche answer is " maybe ". Mig in short circuit transfer is
constant voltage. And TIG is constant current. But MIG is pretty much
constant current in Spray Mode. Think about it.
Constant stream of ionized particles.

When stick welding you are using spray mode. Unless you are a really
bad welder, you are not doing short circuit transfer.

So there is no reason you can't do wire feed welding with a constant
current supply. I have a friend ( Sorry Steve, but I really do have
some friends ) who said he used his stick welder coupled to his 110
volt MIG welder when the metal was too thick for his little 110 volt
welder. I did not think it would work and thought he was pulling my
leg. But tried it, and it is possible. It is even possible to use a
AC arc welder with a non-voltage sensing wire feed, but I think DC
would be a lot better.

Yes this sounds like a bunch of horse pucky, but you can try this at
home. Caution if the wire feed speed is not fast enough, you might
lose a contact tip or two. So start with a fairly high wire speed.

Now whether the Harbor Freight welder will supply enough current, I
don't know.

Dan