It is absolutely doable. I took A & P 1 with almost no background in Chemistry (besides taking general chem in 10th grade) and I passed the class with an A. I am currently doing A & P 2 and taking chemistry and again it is very doable without chem. While it definetely helps to know chemistry while taking A & P in my class she does not require that we know anything chem related.
Currently my GPA is 4.0 with A&P 1, Microbiology, Statistics, Speech 101, and Philosophy. I am finishing up my pre-reqs this semester. Currently an A in Chemistry and A&P, and no clue about my English class...
I currently live with my parents and commute to school, I also work part time Fri (half day) and Saturday (full day) at a hardware store in order to save up money when I am going to move. It's stressful but definetely doable. I know many people in my school who have it much worse than I do.
Currently taking Chemistry right now (Spring Semester), never did like Chem, however it's going pretty good. I have about a month left until the semester is over. Hopefully all will go well, good luck to you.
When I took A&P 1 last semester the lab was pretty useless. All we did was a 10 point quiz and dissections or general labs. It all really depends on the lab and your professor but I am sure if you talk to your professor he/she will understand and let you make up the work. Usually the first lab session is nothing more than introductions and basic lab rules. I highly doubt you will do anything anatomy related; at least that was the case in my class. Good luck..