Does osek b’mitzvah potur b’mitzvah (one who is occupied with a mitzvah is exempt from other mitzvos) kick in when a charity collector asks for tzedakah from somebody who is learning Torah?
No. If a poor person or charity collector approaches somebody while he is learning Torah, he is obligated to give tzedakah, and the fact that he is occupied in Torah study does not provide him with an exemption.
The reason for this is that unlike other mitzvos, the study of Torah does not exempt a person from the performance of other mitzvos that cannot be performed by other people. Giving charity is a personal obligation that cannot be fulfilled by others, and therefore the study of Torah does not exempt the person from his obligation.
See Birchei Yosef, Orach Chaim 38:7; Shulchan Aruch, Yoreh De’ah 246:18.