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Will breaking your wrist early in your swing cause you to lose distance? It seems like I'm breaking my wrist as soon as I take the club back, and I feel like this is causing me to lose distance on my shots? What do you think?

Cocking the wrists should start about about halfway up the backswing, not immediately when taking the club back. Cocking the wrists immediately might cost you accuracy and distance. If you let the cocking of the wrists happen later (it is not necessarily something you do purposefully), it puts you in a better position at the top. It is almost impossible to explain why (for me anyways): Sorry. Try it out though!

Early wrist cock promotes a steeper swing, narrower width which is manifested in less distance and more spin...

Hank Haney video on the topic.

Are there any drills I could do on the practice range to promote a one piece takeaway and prevent me from breaking my wrists early?

I recommend that you watch Tiger's takeaway, backswing move at least 10 times, and then try to copy it, using a mirror. That part of his 'swingportrait' video is actually one of my favorite swing-thoughts.

YouTube Video

That clip never gets old...literally poetry in motion...