If a client cancels a booking due to an unfortunate circumstance that happened between them and the sitter, will they still be able to leave a review?

Of course they can leave you a review. The job was booked and they have the right to leave you a negative review because you did not perform the services they expected.

I noticed in your profile you have a whole disclaimer paragraph about your primary job in the ER and how unpredictable it can be. I don't know if it was always there, but it would be in your best interest to go over those details before you book any jobs to ensure that pet owners understand. Make sure you get it in writing through Rover's messaging system so there's no he said/she said.

I"m not 100% certain but I believe they can leave a review as the booking had already started and was canceled mid-way. If you are lucky they won't leave one! Providing care at the times you committed to is very important if you are to continue as a pet care provider, best of luck in the future