It might depend on the drugs they can offer you if you need them, and what needs doing. But I can't see it being a problem. Could you not phone them up and speak to them about it or make an appointment at least to see what they say?
I was at dentist yest with gum.infection. No x-ray as pregnant and no antibiotics for me as they can only give amoxicillin in pregnant and I'm allergic. I had a deep clean and scaling done with local anaesthetic.
I was lucky enough to snap my molar in half last week, I've seen the dentist twice since and he wants to wait until baby is here before removing the tooth as it can't be fixed... (thanks for that pregnancy )
I had a scale and polish yesterday, no local anesthetic though but to be honest it didn't hurt and I was expecting it to kill!
I had a tooth removed around 30 weeks maybe further. I was booked in for a filling at 37 weeks but ended up cancelling I was took in the same day to be induced. Baby is now 5 months and I still haven't made another appointment so if I were you I'd do it now it's not that I've not had the time just hate the dentist