Mmmmmaybe? He might just want to confirm its history, see if it's eligible for any recalls, or find out if it has been reported as stolen (there are databases).
Orrrr he might want the serial number so he can create a fraudulent service record for a phone he already has and just needs a known "good" serial to do so.
If you're worried, you can give the serial number but leave out the middle 4 digits. Just make sure to include the first 4 and the last 3-4. You can do dashes for the rest, like W802----D7H or something. If it's an 11-digit serial, you should only need to include the last 3. If it's a 12-digit, you should include the last 4. Those last digits would let the person confirm exactly what model/make/size phone it is, and the first few will say when/where it was manufactured.
--Patrick