A given 13-year-old might want to, and if circumstances allow it to work - and to no one's detriment, and hers and his happiness and benefit - then why on earth not? (Why, indeed?)
To be "involved" with a 13-year-old is a different question with perhaps the same answer but to the nth.
Of course, any narrow-minded person will just formulate a false answer based on a very specific imagined scenario where the results are detrimental and apply that as logic to ALL scenarios that share similar starting attributes on a surface level even if on a much deeper level is where the results start to diverge.
At the end of the day, it's treating girls like property that we should have a problem with because that (along with many other truly bad ideas) is what causes the "bad outcomes", not the freedom to marry itself let alone the freedom to be fully human and pursue meaningful relationships with people of her choosing - emotional, physical, romantic, spiritual; and, of course, we know that even friendships come under fire as a side-effect.