No; it'll probably slow your learning of both layouts since there are enough similarities between the two to keep you confused.  I'd recommend learning Qwerty first, since it's everywhere.  It's pretty easy to dismiss that advantage until you know Qwerty and then temporarily lose it for some reason, I've discovered the hard way.

Well, I learned touchtyping using a program like TypeFaster. I learned to touchtype when I learned Colemak, and I sorta touch-typed on QWERTY. Except that I used three fingers. I can touchtype now on both by looking down for QWERTY and not as fast. But still it works for my purposes. What you should worry about mostly is practicing, and getting used to the fingerings.

Also make sure to look up any alternate fingerings as they are very useful in QWERTY (more so than in Colemak). And any distant keys make sure to accent your fingering with your arms. It used to be difficult for me to reach Y in QWERTY or J in colemak, but I tend to move my arm for that letter and it becomes easy once your used to it.

I got to be 50 wpm sometime around after 3 months in QWERTY, but in Colemak, since I could pretty much touch-type already, and I just needed to learn the layout, it only took me about one month. But it varies with different people considering their mind and the anatomy of their fingers, and also the comfort level that some keys provide.

When reaching for X, C, V, or B, I tend to anchor my left hand to the home row with my pinkie (i.e., keep my pinkie on the A key), and move the rest of my fingers down.  I don't literally rest all those fingers on the bottom row, I just pick them up off the home row and let them naturally "float" down a bit with the finger that needs to hit the key.  The key word here is "natural."  The only thing you should have to "force" is keeping your pinkie rooted to A.  Keeping the pinkie on the A key will help you return the rest of the fingers to the home row without looking.  Actually, these days I often float all the fingers, especially on the right hand, but that's not something that would be expected of someone just starting out.  :)

I seem to remember it taking me three or four months to hit 50 WPM (on easy stuff) when I first learned Qwerty.  I could already hunt and peck at around 35 WPM (on easy stuff), so most of that was learning touch typing technique.