Obviously. The idea being that the police aren't going to be going through random wallets to spot 20's to find the missing millions. Serial numbers aren't scanned at registers. The actual stolen money would never be found if it's already been distributed amongst the population. They are looking for a large sum of money being held by one entity, not a random bill.So instead you are slipping them illegally obtained money that might be flagged?
Still you wouldn't want to be careless with your pile of money. If someone happens to find it in your mattress at the end of 20 years, and none of the serial numbers match, and nothing else ties you to the crime, would they prosecute? How would they prove anything though? You wouldn't need an alibi, there would be no security tapes to pinpoint a time or anything. Maybe if the amount matched nearly exactly, but I'm sure you'd have that possibility covered.
Keep in mind this isn't my fantasy. I was only entertaining others' fantasies of it. Perhaps I'd consider trying if I did get bored at some point, but it's not my first thought. Personally I think I would consider burying it and make a treasure map for someone to find. Or sticking a wad of it in a bunch of homeless people's cups. Who knows if after 20 years you'd still even be your present day self anymore. Maybe we'd all be crazy and just start trying to flip the world on it's head as much as possible. Watch the world burn.