Depends on how you configured the HSRP, If you followed the best practice, Active router always be the path for the outgoing traffic.
HSRP group you will need to use the priority command.
The default priority is 100.
The higher priority will determine which router is active.
If both routers are set to the same priority, the first router to come up will be the active router.
Assuming you mean traffic arriving on another interface on the standby router then no because the standby router has directly connected interfaces in the HSRP enabled subnets.
Is there a reason you want to do this ?