To answer the original question.
Would doubling your output power about 4 times increase your 'range' by about 4 times? I'd have to say it -might- be a possibility, but it also might not be. You can't estimate 'range' by power output. While power does have a part in that, it certainly isn't going to make all of, or even most of the difference in increasing/decreasing how far you can talk.
The one thing that determines range the most is propagation, which you/I/we have no control over at all. Of the several things we do have control over, the most likely 'thing' which can increase range is the antenna (as everyone has already said). Maybe the next thing is output power. And one part most people don't think about, is the receiver you have (radio). If you can't hear'em, it doesn't matter if they can hear you or not, you still won't be able to talk to them. Which is the whole point (unless you're doing the shoot-out thingy, and then you don't need a receiver for that at all. Do you?).
All antennas are not created 'equal', and where they are can certainly make a difference too. The majority of thought is that your antenna won't 'handle' that 110 watts. I sort of have a feeling that it could, but no idea if it -would-. It's power handling ability isn't what's in question (much).
How much you plan to feed that amplifier is also questioned, and I think that's certainly something to think about. Most transistors can be 'tickled' with less power than most people realize. And since you've doubled your radio's 'normal' power for extended range, you may want to 'un-double' it to feed an amplifier. Too much 'tickling' isn't funny any more, it's called torture, it harms the amplifier.
All of this is sort of thinking "out of the box", right? No big deal until -not- thinking "out of the box" ends up making you think "I'm out'a 'bucks'!".
- 'Doc