Yes I've always done that, it's good practice from an infection control point of view and I like the boundary between my time and work time signified by what clothes I'm wearing.
Hospital staff wear "smart scrubs" they are our personal uniform and we bring them in and take them home, where as the docs and theatre staff use the hospital scrubs that go to the laundry at the end of the day.
We now have special scrub bags to transport our uniforms and they go straight into the washing machine, bag and all.
Apologies for the fucking boring details