Do it.
I learned the hard way with DC1. If I'd lied about my ovulation day (it was day 29, was temperature charting and got a BFP at 9dpo so very sure!) they'd have not adjust my dates. Instead they set them to what she measured at 6w5d, which was 6w2d. So my due date ended up being 3 days later.
You'd think it wouldn't matter, but I wanted a homebirth. At 36w6d I went into precipitous labour. As I was literally SIX hours short of the 37 week cut off they made me go in to hospital. The panic of the sudden labour and the ambulance transfer (I'd never been in an ambulance before) meant labour stalled and I didn't dilate fully. The incompetent bank midwife at the hospital told me to push and I didn't really feel like I needed to, but I did. For an hour. Whilst she yelled at me I wasn't trying hard enough.
After an hour she checked me and it turned out I'd been pushing against a lip. She moved it out the way and DC1 was born shortly after. She then administered the injection, which I later found out shouldn't be done with a precipitous labour as the uterus is too exhausted to push it out. Manual traction was involved, she claimed she got it all. We went home the next morning.
12 days later I spent three nights back in hospital with a postnatal haemorrhage and infection (guess she didn't get it all) on an IV.
A few years later I nearly lost DC2, it was just luck I had a cervical length check at 18 weeks and got an emergency stitch. DC1's birth basically trashed my cervix and I now have a permanent stitch placed through major surgery as of DC3 which I had to fight for but it turned out I definitely needed, this is DC4 and I will have had 3 c-sections. Major impact on my life and nearly cost me my children.
If I'd just lied about my dates at the beginning none of that would have happened, I would have had my homebirth with the nice community midwife who would never have rushed me into pushing when not ready nor administered the injection. When I talked to them about the birth when I was pregnant with DC2 they were not impressed with that bank staff hospital midwife at all.
I tell every woman to lie if she is sure of her ovulation because of the huge difference it can make. DC1 was ready to come, it was her time, a homebirth would have been perfectly safe, but they all thought she was early and she wasn't.