if it is only capable of supporting 1333 and you replace it with 1600 the 1600 will run at 1333 speeds I doubt you will notice a difference between the two speeds unless you are a pc fanatic and need every millisecond.
Couldn't agree more with usafret that's why I asked why buy a all in one pc its money in the trash its only a tempory fix when you have so many other options out there why worry about ram speeds with its a all in one not trying to be nasty but in a way its silly somewhat cuz you cant upgrade them.
an AIO type pc is really only usefull for an office/web browsing machine that you dont plan on upgrading. if your pc requirements are very low then this is a cheap way to go.
however, if you plan on doing anything else you want a box period. even if your needs are low i would still suggest a box since if you did want to upgrade later you can.
think about it like a car where the tires go bald and you cant replace them because they are welded on. the only thing you can do is get a new one. a box pc is like a regular car where you could just put new tires on and get some extra mileage on it even if the car is old and less than ideal