No, it isn't.
See you, goodbye = ci vediamo, ciao (we'll see each other, goodbye).
See you soon/later = a presto/a dopo (arrivederci)
See you in March = ci vediamo a marzo (we'll see each other in March)
There are a few other options here...
Te vedo! - This is okay in some dialects but you definitely won't hear it from your professoressa d'italiano
Vedo te! - This is also okay but often used for emphasis (I see YOU, not him!)
Stick to Ti vedo! :)
no, on the opening of clitics is an introduction ": in most tenses they must go before the verb and after non if present. If there is more than one clitic, the indirect one comes before the direct one, and often changes its form." According to that, it must be ti vedo or non ti vedo.
Should "You I see" be accepted? English is often used in both ways. For example, if I met two people at a C++ conference, one a programmer and the other an artist, I might say to the programmer, "You I understand," and then to the artist, "but why are YOU here?" The "You I understand" could have also been "I understand you," but both work.
By saying, "You I understand," you are emphasizing "you." In the Italian sentence, in order to emphasize "I see YOU," (In English, YOU I see) you would say instead "vedo te."
For real, why do they have clitic and whatever the other one was called pronouns? Of all the languages I know some of, I have never come across it before