Can I continue to play basketball if I've torn my mcl?

Yes. Yes but not until after it heals, which may take 2-4 weeks for a grade 1 sprain, 4-6 weeks for a grade 2 partial tear, or 6-8 weeks for a full thickness tear. Returning to play prematurely may worsen the injury, delay the healing, or lead to additional injuries from a still unstable knee.
Soon. Assuming that you are being treated conservatively with bracing and pt, you are probably hanging up the high-tops for 3 months or more.