Is this a run on sentence you and I and the whole team will go?

No. That is just a style problem with the multiple subject, and is acceptable.

Another form is "You, I, and the whole team will go."

A run-on sentence includes more than one thought without using conjunctions to set them apart.

Example :

The dog ran past me he was chasing the cat. (run-on)

A comma does nothing to fix it.

The dog ran past me, he was chasing the cat. (run-on, comma splice)

Two ways it can be fixed :

The dog ran past me. He was chasing the cat.

The dog ran past me as he was chasing the cat.