If the Eastern US were a desert just like the southwest, would the east coast have a Mediterranean climate?

No, because the east coast of the US is on the western hemisphere, adhering to western hemisphere climate..

The northeast has a more southern canadian climate, while the southeast has a more Caribbean influenced climate.

This is in truth brutal winters up in the northeast, and mildly hot summers.

And in the southeast, mild winters, but with disgustingly nauseating summers with violent, horrifying nighttime storms, and sometimes a hurricane.

Which is more tolerable ?

By far, the northeast.

If the east coast were a desert, that automatically means arid and bone dry.

Average temperatures would be hotter because nothing there would exist to cool it off...

Or to support plant life..and therefore animal life, including us.

Deserts exist because it lacks rainfall.

That's how important to life, a balanced, and seasonal climate is.

The fact is, without rain or seasons anywhere in the world, you'd die.

Therefore In theory, Florida would therefore be the great beacon of the good life right ?

WRONG.

Because entire complete opposites do not effectively answer each other in life..

There has has to be a balance, in order to thrive.

The best balance that you find on the east coast, exists anywhere from New York, to about Virginia and Maryland.

When you start hitting the Carolinas on your way south, you start seeing a progressive increase in problem weather.

The Mediterranean climate is characterized by mild winters and moderate summers. Not very desert-like at all. Deserts, at least the ones with low humidity, fluctuate greatly, even on a daily basis.