I'm not sure what "thanks regardless" is supposed to mean.
Thank you, regardless of whether you can help me [in the future]: the better way to say this is "Thank you in advance" or "Thanks in advance"; but given that that's what you wrote at the end of your question, it seems you believe "thanks regardless" means something else.
Thanks anyway: this would definitely not be an appropriate close to a message. You would use it if someone had just said "no" to a request, and you wanted to be polite (or wanted to appear to be polite).
Edit: thanks for the link. I've looked at the query which prompted this question, and given that context (asking a question and then finding out something which makes it moot) I actually think "thanks regardless" is an OK phrase - as in, it's grammatical and it makes sense. However, I think Remou's suggestion of "Thanks for all the replies" is more polite.
[Note that Stack Exchange etiquette doesn't require, and possibly even frowns upon, conversational noise such as "Thanks in advance".]