Do it! I went into labour with my first in the middle of a work meeting at 38 weeks, and I haven't been able to put my feet up in the 5 years since 
Things I would have done in hindsight with 3 weeks:
Sorted my wardrobe to get the post baby stuff ready - not so much about moving all the maternity stuff away (depending on how your shape has changed, some of that might be good for longer than you'd like!), but getting bfing-friendly tops out and the like.
On a similar vein, going to a bfing group - mothers to be are welcomed and with more support I definitely would have ended up bfing DS1 for 18 months like my next 2 DCs instead of a miserable and nearly PND-inducing 5 weeks.
Had coffee with all my friends, especially the single or work-related ones who might be tricky to stay in touch with for the first bleary weeks 6 months, depending on what sort of baby you have, (and what sort of mum you are). If your mum or other doting relatives are around, this can be a lovely time to sit and reminisce about baby and birthing stories, my older family members loved to share, and I suddenly found the stories a lot more interesting! If great aunt flora shares a horrible tale with Game of Thrones levels of blood and torture just block your ears and mutter "epidural epidural epidural" until it stops 
Gone to lots of movies, you are unlikely to be doing this for a while!
Go on lovely long wanders to help with fluid retention (and the final-trimester chocolate cravings) while daydreaming idly about your perfect progeny --and hoping to god that this might kick-start the process.
If it's fun for you, cooking lots of one-hand-able meals for the freezer for the first few weeks. Or otherwise, sorting out deliveries and/or making a takeaway roster for DH.
I also wish that I had started my pelvic floor and relaxation exercises properly, and wish I had NOT spent so much time making the fecking nursery, which was unused for nearly a year anyway as all my babies liked to sleep in our room (and ideally in our bed) and play within a 2 metre radius of our feet.
Or even just sit for 3 weeks with your feet up and watch TV boxsets. If you're feeling well, it's a lovely and exciting little pause, and if you're feeling crap, you'll need the rest! Your job is stressful enough and your timing sounds great, good luck 