$2-300 is definitely enough to get a mixer with good EQs, if you buy them second hand. A nice Tascam for example. Will it help your mix? Possibly, but you'll also have a lot of extra work. Remember, that analog mixer will have no, or very little automation (My Tascam has mute automation). Every time you are stopping to work on a song, you will have to write up your settings for every channel. And you have to ride the faderswhile mixing. Now, I *like* riding the faders.

But it is a lot of work.
And also, you will have to have a soundcard with many separate outs...
I use an analog mixer, and will continue to do so even though I'm now trying out different DAWs. This is for three and a half reasons:
1. I have a bunch of synths that I like to to sync with the DAW. I could record them, but I don't want to, for a bunch of other reasons, like diskspace, processing power, and the fact that I want to be able to easily rearrange and change things, including tempo, for as long as possible. This means I need a mixer.
2. I already have one.
3. Analog mixing helps "weld" the sound together, by imposing a sound of it's own. Digital filters are clean and transparent, analog are often not. This is of course even more noticeable with analog tape, which I think is the real reason many pros like to track to tape.
In your case, I think it's a waste of money. Why? Because you seem to think it is.

My main rule when it comes to buying equipment is: If you aren't sure you need it, you don't. Use what you have until you can't make it sound any better. Then figure out what is stopping you, and fix that. For example, when I bought my monitors, I realized that what was stopping my recordings from getting better was my crap mixer and my crab reverbs. So I got a better mixer and better reverbs, and now things are much better. Now I need to get better at mixing and recording again, until I get so good that something else stops me from getting better.