No.
A tab is a self contained unit which can have its own main panel, layout style and target panels but you cannot have a query in one TAB direct its output to a different EXISTING TAB.
On a practical note - where would the user know to look for the result?.
You could have your query open its output in a new tab which would then put the focus on the new tab so that the user was shown the results in the new tab without having to navigate to it. The user could then close the new tab once (s)he had finished with it.
There are some html style links you could try - see appendix D of the user manual