Having the 13 year old boy wear youth diapers for bed wetting is a good thing for hygiene as it will keep the 13 year old boys clothes and bed dry and they will be much more comfortable wearing the diaper.
If I were wetting the bed as a 13 year old I would rather wear the diaper for bed wetting and wet the diaper instead of wetting my clothes and bed which is uncomfortable.
I used to wet the bed as a kid and teen but never had the option of wearing diapers and if I did I would have wore the diapers for the bed wetting.
Yes a 13 year old boy or girl who wets the bed can wear diapers for bed wetting if they need them.
Some 13 year old boys may fit in larger size baby diapers such as pampers cruisers size 7 or even pampers cruisers size 8 diapers.
You can also go online to online incontinence supply websites and buy disposable youth diapers that will fit the 13 year old boy easily and will be very absorbent for the bed wetting.
You shouldn't force the 13 year old boy to wear diapers if they do not want too but you can offer them the option of wearing diapers at night for the bed wetting and you can then promise the 13 year old that you will keep it between you and them about the diapers and bed wetting.
If the 13 year old refuses to wear diapers for bed wetting then you can try a mattress protector on the bed that you can remove and wash when the 13 year old gets pee on it.
Or you might try the option of bed wetting underwear such as Goodnites or another brand of bed wetting pull ups.