Yes, possible with SNMP. The TMOS Management Guide (available on support.f5.com) has an overview of how to work with SNMP on BIG-IP devices. Specifically, you'll want to get data from the F5-BIGIP-LOCAL-MIB, in particular "ltmVirtualServStatClientBytesIn" and "ltmVirtualServStatClientBytesIn".
On a BIG-IP device that has SNMP enabled, allowing at least read-only access to a community named "public" you could try the following from the CLI (replace "vs01-http" with your virtual server name):
vip="vs01-http"
snmpget -v2c -c public 127.0.0.1 \
F5-BIGIP-LOCAL-MIB::ltmVirtualServStatClientBytesIn.\"$vip\" \
F5-BIGIP-LOCAL-MIB::ltmVirtualServStatClientBytesOut.\"$vip\"
Nimbostratus