Asking what exactly the coach’s support means isn’t an off putting question for the coach. My guess is he/she is mildly surprised you haven’t asked. NESCAC coaches don’t have money to give. Their only currency is admissions help. They expect to answer that question. I would certainly ask it before I did 15 essays. I would ask it before I did one personally.
I don’t know exactly your athletic level, but S19 had several coaches he was talking to tell him that if his school fell through, they were still very interested. So it is also possible if your ED school doesn’t work out, you may be able to get coach support elsewhere for ED II or RD. My guess is that will be a bit easier to find this year, as many kids are reluctant to ED without having a chance to visit.