YES
In fact, inequalities will be more pronounced because all environmental factors will have been removed from the equation.
You can see this in the world right now. Societies which level the playing field and open it up for everyone find that to be the case.
In such a society as you propose, people would pursue their interests freely, not being limited by needing to earn a living from them. Some would naturally be more talented than others and would excel in those fields.
Then there's that nasty human tendency towards greed, summed up best in the movie Key Largo "I want MORE" Some will be driven to acquire more, some will be content with what they have, which will make inequality GREATER because there will not be a universal motivation to improve one's conditions.
Edited to add from comments:
Want's and needs are two things. Just because you have everything you need, there will still be things you WANT You could be fed a basic diet, housed in an apartment with cinderblock walls and construction, but would rather live in a house by the lake and go fishing because you want to eat the fish you catch yourself.
While needs are fairly universal. (Food, shelter, clothing, medicine) wants are not. I may want a yacht where you may not. You may want a house where I'd be happy in an apartment. Needs may be fairly equal, but wants are not.