In bitcoin world you are anonymous and no one know that who are you and from where are you so you can easily use any mixer without any restriction. no one will find you and the fact is that it is legal in every part where bitcoin is allowed.
Also if you mix your coins, there are risks you'll get coins from people who did illegal shit, not entirely sure about this but it seems logical.
Is this possible? What are the implications of this?
Yes, you could get 'tainted' coins as they are called.
You could be investigated, but I doubt if the authorities will prosecute you.
