Yes, it will indeed!
This kind of activity is called Neurobics, which is essentially doing things you normally do but done differently. Like brushing your teeth with the other hand, taking a shower with your eyes closed, writing with the opposite hand, taking a different route to work, etc.
What happens in your brain while you're doing this becomes a brain exercise because different, underused nerve pathways and connections get activated.
This stimulates the growth of new brain cells and brain connections.
According to the neurobics.com website, to be a neurobic activity it must have one or more of the following:
1) Involve one or more of your senses in a novel context.
2) Engage your attention.
3) Break a routine activity in an unexpected, novel way