How long does it take for doxycycline to take effect for acne?

Yes it does...

Doxycycline is frequently used to treat chronic prostatitis, sinusitis, syphilis, chlamydia, pelvic inflammatory disease, acne and rosacea. In addition it is used in the treatment and prophylaxis of Bacillus anthracis (anthrax) and in prophylaxis against malaria.