It would be entirely possible in this case. At first I thought you had meant abstaining from sex for life or something... O.o; (and attempting to have a relationship).

But yes, absolutely. Relationships do not require sex in order to be successful; sex can help to make a relationship more successful or help to make a relationship feel complete, but it's not necessary to build a good relationship at all.

Would it be too bold of me to ask why you were curious?

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