Broke left wrist and right elbow June 2009, back on the bike Easter 2010, but the elbow was worse than the wrist and took 6 months just to start healing.
Once you have surgery the break is technically ‘fixed’ but it’ll be sore for a few weeks and you don’t want to risk the wound getting infected anyway. I’d give it 4 weeks from surgery – start small, you don’t want to find out it gives you eye watering pain half way down 50 shades of Black, I’d personally try to mitigate the chance of landing on it again for 6-8 weeks post surgery at least.
It’s very unusual for NHS to remove a plate unless it’s causing you problems, too great a risk of infection for no reward. I’ve had my elbow plate out, but wrist is still in 6 years later. Hurts first thing in the morning if it’s cold and if I ride a lot of rough stuff – had an uplift day at Antur Stiniog last week, was killing me by 4pm, took 2 pints to sort it 😉