Yes, it is indeed possible.
I assume that 10.1.1.0/24 is the ip pool subnet that the VPN Client gets assigned, so here is what you would need to configure:
1) If you configure split tunnel for the RA VPN, you would need to include both 192.168.1.0/24 and 10.2.2.0/24 in your split tunnel acl.
2) Crypto ACL for the P2P VPN would need to include the following to define the interesting traffic from the vpn client pool subnet:
On Cisco IOS (HQ): crypto ACL to also include from source: 10.1.1.0/24 to destination 10.2.2.0/24
On the remote router: crypto ACL to also include from source: 10.2.2.0/24 to destination 10.1.1.0/24
3) If you configure NAT exemption on the remote router, you would also need to add NAT exemption between 10.2.2.0/24 towards 10.1.1.0/24.
Hope this helps.