I married a BT from a wonderful, albeit totally frei family. Go into a shidduch, ANY shidduch, with open eyes and ears. He may be the perfect guy for you, or for reasons that may resonate only with you, not be a good choice. When you marry someone, you DO marry his family, upbringing, extended family as well, unless you live so far away from the irreligious relatives, that they have no impact on you.
Still, I would not have married my husband had he not had the middos that he observed in his parents’ home. So you need to find out about the family situation – are they supportive of his frumkeit (VERY important to know this in advance), or will they give you grief the first time you do not attend a family Bar Mitzvah that is more bar than mitzvah? Are they good people bein adam l’chaveiro. Is the ONLY negative that they are not shomrei Shabbos? If the answers to these questions are in concert with what you are looking for, then go for it. A boy who is frum from age 13, sounds solid to me.