Yes on all accounts
Whoa there. Not necessarily. And in fact, if we're talking about this circuit ...

the answer is very likely to be that a reverse audio is the correct taper.
R4 sets the limit on the gain. R4 + the gain pot's value divided by the 1M in the feedback loop will give you the total gain, so it goes from just under 2x (1,000,000/504,700) up to 1,000,000/4,700 = 200x.
Smaller resistances increase the gain, and as the resistance to ground approaches 0, a smaller change in resistance is required to increase the gain. It's a logarithmic relationship. You can see this by setting the resistance at, say, half on a linear pot:
1,000,000/250,000 = 4x (we only have twice as much gain with half a turn!)
And then 3/4:
1,000,000/125,000 = 8X (see how we have TWICE as much gain with only 1/4 turn?
... 15/16:
1,000,000/31,250 = 32X
Anyway, I think you get the idea. The smaller the resistance becomes, the more quickly the gain scales up.
A linear would probably bunch up the gain a lot, and an audio taper will be a very poor choice.
The gain pot in the fuzz face is similar, and most people agree that a 1KC is the correct choice there.
Unless you actually disliked the taper in the pedal to begin with, use the reverse audio again.