Short answer (Shwetambar, Murtipujak context):

• No. When a woman is menstruating (rājostā) she generally does not participate in temple puja involving murti (murtipujak), and she does not take part in Samvatsari Pratikraman at the temple.
• She can resume participation after the period ends and she becomes pure again, typically after the fourth day (on the fourth day of her cycle) when she has performed the customary purification bath (shuddhi). From that point she may rejoin temple rites and Samvatsari activities.

Different Jain traditions recognize slight variations:

• Shwetambar Murtipujak: emphasis on not performing murti-puja and not attending temple rites during the menstrual period; can re-enter after shuddhi.
• Digambar: similar general guideline of avoiding certain temple rituals during menstruation, with possible minor differences in the exact list of restricted activities.

If you would like, I can point to a JainKnowledge page that covers Samvatsari and prakritraman practices.