I was given a continental round trip voucher by US for volunteering in an overbooking situation. Will I earn miles when using this voucher?

Thanks!

No. Additionally you need to find seats in the X bucket which are the same bucket as the saver award seats come from. However, you do not need a Saturday night stay on a RTFC itin. Alternatively these go for ca. $225 to $250 on eBay and with the proceeds you can buy a ticket that earns miles and allows upgrades.