As a dm I would dislike this greatly as it causes the DM several headaches.
(1) you’d have extra gold and magic items as a resource, that leads to needing to do extra effort to balance encounters for your different resources
(2) unless other PCs have that level, you’ll be unbalanced in resources than others
(3) will the in character talk devolve in to needing to justify whether it is right for the party to know stolen gold is being spent?
(4) you are getting a strong starting character benefit with access to lots of gold to buy stuff/favors/bribes/etc. but no downside unless the dm wants to work in someone trying to chase you down at minimum a number of times the stolen money gets used. That means needing to justify how someone finds out and just possibly making it take spot light very often ( I would get very tired of that eventually from either side of the dm screen)
That said, I am speaking about ME. If your DM is on board and it will be fun for the WHOLE group, then have fun with it.
As an aside, you could circumvent SOME of this by removing the liquidity of it: maybe pregame the money is used to buy a small estate in the country side making it a headquarters for the party ( or a remote countryside barony gets purchased making them a land owner now that has to keep their barony clear of monsters etc) that type of stuff turns the funds in to a party-wide story point even if it originated as your individual PCs background.