Yes its possible. You have a default route at your Branch office pointing towards the HQ, the HQ office would have static route for the subnet you've allocated for the Branch office.
Since the site has only one WAN link, you don't get any benefits from the routing protocol in the event of link failure.
The only drawback is limits on scalability and the associated administrative burden. If you add another branch office, you will need to manually update the routing table etc. If this ends up at 100 sites you might want an IGP.
I should note I've assumed you allocated one large subnet to your branch. If someone setup something silly like 20 non-contiguous IP subnets to the Branch office (I've seen something similar) you might want to consider IGP. You also need to redistribute the static default route into OSPF which is straight forward.