You are worried about him not knowing you care ... But meanwhile it seems very clear he doesn't care about you. (Or at least he cares more about drinking than you.)
Sending this letter will not make you feel any less in limbo. You're giving him the power to hurt you all over again. And your just going to have to start the healing all over again.
Even if he gives you a positive response, that will mean nothing, as he did not take the initiative.