Yes, you could. but thats not only a question of the combat routine. Even some CR's (Combat Routines) can manage it alone. It is also a question of your BotBase.
Combat bot for example lets you run. As soon as you are engaged in combat, Combatbot jumps in, and does the movement for you. If faces targets, runs to range.
Raidbot does it different. with the same combat routine, you have full control of the movement. It will not face the target, it will not move your character to combat distance. you have to do it.
Questing is another Botbase, which will do absolutely all movement for you. Gatherbot/Grindbot too.
As you see, you can do everything you like. with almost all CR's. Depending on which BotBase you choose.
If you want to run BG's and take movement for your charakter alone, chose raidbot. You can also do it with combat bot.
there are 1000 possibilities with Honorbuddy.