Can Triathlon bikes convert to a Cyclocross bike?

New to cycling. Saw some really nice Triathlon set ups but want to ride them on city roads that are not made for Triathlon bikes.

I know they are made for perfect roads so can I put suitable tires on them or is the frame simply not meant for rough roads. Also can I still use Aero handle bars or will I fly over them on the first rough bump?

I'm not competing just want to work out hard and don't want any limitations like rough surfaces. I really like these Tri frames and handle bar set ups.

ddub

Regarding the tires, generally, no ...

CX tires are generally about 700x30+ ...

However, there are TUBULAR/(sew-up) CX tires, the size can be as small as 700x25 ... I used to have a pair. They are NOT intended for rough pavement ... neither are "regular" CX tires, in general.

I doubt the Triathlon bikes you are looking at can fit a tire larger than 700x28, possibly no larger than 700x25 BECAUSE of the clearance limitations of most front forks ... particularly, if you are actually referring to a TT bike.

If you are referring to a TT bike, is it the vertical seatpost OR the handlebars OR both that strike your fancy?

Regarding the handlebars, the only reason you would possibly fly over the bars is if you leave your front wheel in a pot hole ... however, you would probably NOT want to have your hands on the aero portion of your handlebars if you encounter a rough patch of roadway because there would be less benefit of being in a tuck position compared with the benefit of having a stable bike ...

Some bars used to have more drop than others, BTW.

If you want a really invigorating workout, then buy a bike from Wally World and put some TT bars on it.

A tri frame will won't be much fun in the city and will throw you in the dirt first chance it gets.

You need an all-around road bike that will handle dirt. Check out the Specialized Tri-Cross range. It's a cyclocross bike with relaxed geometry, cantilever brakes, fat wheels, and ample clearances for mud and snow, that's been set up for recreational riding and touring, using triple chainwheels and plenty of eyelets for attaching racks and fenders.

Then if you still have the jones for an aero crouch, bolt on a clip-on handlebar.

I would think that a tri bike would be quite unstable or "twitchy" in the conditions you mention, not to mention uncomfortable.