So the correct sentence would be:
Domo arigato gozaimasu soshite do itashi mashite.
??
I don't think I'll ever have the need for Japanese, but I have a dozen or so of the Rosetta Stone language CDs, Japanese is one of them and I haven't reviewed it in years.
It is gramatically correct, but sounds a little odd strung together that way. You probably would not add the “and” in a Japanese sense. Japanese is a tough one.