how can I practice getting fully in time with the drums on a track
It's doable. We had a similar situation in one project, and with some preparation it ended up sounding great. Depending on what you are doing, it might be more trouble than it's worth, but if you really want and/or need to do it, you can.
First of all, if the drum part was played by a human, you need to quantize. Otherwise you'd need to adjust to the performer's imperfections, which makes this many times harder (perhaps not even feasible) to do.
I used Ableton Live's warping for the quantizing, but all the top DAWs have tools for doing this. Because this is a complete track with many elements, you'll need something like Logic's Flex Time, Pro Tools' Elastic Audio, or Live's Warping (as opposed to audio cuts, where the cuts would be easily audible).
You don't have to quantize every hit, you can get away with quantizing to every beat, perhaps to eighths at most (if there's swing in something, you can bring it back with quantizing).
Now that the track is consistent in time you'll be dealing only with one time variant (you), not two (you and the other performer).
After that it's all about practice, you need to have very solid timing. If you are not used to play with a click this will be more difficult, but still feasible with enough practice.
In our project we had a very good drummer, that was used to play with click. Once the track was quantized he managed to pull off a great performance, but he was struggling with the non-quantized track.
how much would this 'double hit' effect show up if I was playing an acoustic set live to a recorded backing track
Not at all, if your timing is good enough. There isn't much room for error, though.
In my experience (so this is purely anecdotal) the ideal difference range (how much time you can differ from the recorded drums) is around -+4 milliseconds, so you have 8 ms of error range. From -+5 to 7 ms it still sounds fine, but some good ears might catch some subtle mistakes here and there, so 14 ms of error range might still be enough. At around -+8 to 10 ms the difference starts to be perceived as two separate sounds, so you want to stay away from that.