By "marry" I mean getting into a long-lasting, if not permanent relationship with a partner.
Discussion
Your definition should probably be a little more specific. Am I married to my patent attorney? He has been my (business) partner for several years.
Also, as you've defined "marry" there's no notion of reproduction, social approval or government recognition. Which means faggots have always been able to marry each other (under your definition).
Only if he agrees to the notion that you've married him. Partner can mean many things.
I agree with what you said about them always being able to marry because that's true under common law. However, they have not always been able to until fairly recent under statutory marriage i.e marriage licenses.
How does a lack of a marriage license prevent a faggot from having a long-lasting or permanent relationship?