No. It’s nicotine that causes those risks, not just the effects of burning plant matter in general. Nicotine constricts blood vessels and makes platelets more inclined to stick together; THC relaxes blood vessels and may actually reduce clot risk.
However, I couldn’t find any reliable sources on other risks from combining weed and birth control pills, so I can’t say it’s risk-free, only that it probably won’t cause blood clots.