Absolutely yes, because the most severe risks are associated with the bacteria reaching the heart and into the nervous system, which is a relatively slow process. There's a window of a couple of weeks.

If you could know as soon as you were bitten whether there was any risk of infection at all, that would be very valuable information.

I think it's only a one in ten chance that an infected tick would transmit the infection, anyway. But you would know whether you needed to even book an appointment.