This has been discussed a lot in the past, so I'm just going to say: unless you want to put script tiles on every tile in a single town, then no.
You can also try With a Level script, but there will be a slight delay before you can move after every step you take to let the sprite to follow you, and if you have running shoes or even a bike, the sprite will eventually be far away behind you.
If you do try this, you need to take in account that the player can get trapped if he/she walks into a 1-block tall "hallway."
Even then, you can't transfer the sprite from map to map consistently.
(Don't quote me on this, since I haven't tried it myself. But from the threads I've read about it, it is very difficult to get a smooth map transition and make it work perfectly.)