No. The automated post bans for low-quality content are separated per-site. Therefore, each site pretty much knows nothing about your activities on other sites.
Here's an example: I get post banned on Physics. I then begin providing extremely high quality contributions on English Language and Usage. What does this say? It means that I know how to ask high-quality questions about English. It does not, however, mean I know how to write good Physics questions.
What you need to do is edit your existing questions and answers and try to get some upvotes on them. Once the system gets enough indications that you are providing high-quality content, you will be unbanned.