If I paid to have a window replaced on my car, can I submit the receipt to my insurance company for reimbursement?

Since you are in California, glass claims should not impact your rate. You will want to make sure your policy includes comprehensive coverage (which it should since you are leasing the vehicle). If the cost to replace the window is less than your deductible, however, you aren't likely to be compensated for the window replacement. Or you may have separate glass coverage on your policy. I would recommend contacting your insurance company to ask specifically about how glass is covered by your policy since it shouldn't be held against you.