When "many a [singular noun]" is the subject it is correctly used with singular concordance:
"Many a woman has a past, but I am told that she has at least a dozen, and that they all fit." —Oscar Wilde
So I agree with Loob's point in general, but I also agree with Danster that it sounds odd here. I think, however, that this is because there is a conflict in the statement. "Many a..." is indefinite and general, but by using "especially if" you are making the subject particular. You might get round it by breaking with "many a..." by using a pronoun that doesn't directly refer to it, e.g. "those":
"He courted many a woman at the beach, especially those [women] who already had company."
You might also consider not using "many a..." at all, because I think you are trying to fit it where it does not really belong.
Thank you all for your great comments! I love the suggestion to use "those" and it's always good to see an Oscar Wilde quote. As for formal or less so . . . sometimes I feel "many a" sounds right, particularly if the tone of the narrator changes to more sarcastic, for instance, about someone's exploits.