Yes, but in very limited circumstances. The report has to be within 12 hours (otherwise it would just be a normal LC trip assignment), but greater than 10 hours from notification. That way you would have your 10 hours of "rest" prior to report.

To sum it up, you can get a GS as LC pilot if scheduling gives you a trip that signs in greater than 10:01 from the time of contact up to 11:59 from the time of contact.

Make sure you also look at 23.U.1.B Note two:

"A reserve pilot awarded a GS rotation in which all duty periods of the rotation are scheduled to operate on on-call days may request that one X-day that coincides with a day on which the pilot does not have a duty period within the GS rotation be moved to the first day of the GS rotation."