You can try, but whether it gets through depends on the facility and how the mailroom staff evaluates it.
Most prisons and jails allow hand-drawn artwork to be sent through the mail as long as it does not raise any red flags during inspection. The concern on the mailroom's end is not the drawing itself but the materials used to create it. Certain substances have been used to saturate paper and smuggle drugs into facilities, and mailroom staff are trained to be alert to anything that looks or feels unusual. Thicker paper, textured surfaces, or paper that smells different from standard stock can trigger additional scrutiny or an outright rejection even if the drawing is entirely innocent.
Sketchbook paper is heavier and has a different feel than standard printer or notebook paper. That alone may cause it to get flagged depending on how thorough the facility's mail screening is. Standard white paper is the safest bet for getting something through without complications.
The safer alternative is to send your drawing through InmateAid's photo service by scanning or photographing it and submitting it as an image. It gets printed on standard photo paper and delivered through the normal mail channel without the uncertainty of whether the original materials will pass inspection. Your boyfriend gets to keep it, and there is no risk of it being rejected at the door.
If you want to try sending the original, keep the paper as standard as possible and avoid anything that could look unusual to someone screening mail.