Now I would like to do functional connectivity analysis.
What measure "connectivity" are you referring to?
If you are interested about coherence or phase locking value, you should not compute a time-frequency decomposition with wavelets before, the frequency analysis is included in the computation of the connectivity measure. For instance, run the coherence 1xN directly on your source files.
can I compute connectivity using the averaged data in time domain?
You should not try to do any frequency, time-frequency or connectivity analysis on averaged signals. Averaging destroys the fine dynamics of the signals you try to explore with these measures.
Could I calculate the whole brain connectivity in the frequency domain?
If you are expecting to compute a 15000 x15000 x Nfrequency connectivity matrix: no, this is too big of a matrix to be handled by most computers. You should narrow your search based on the hypotheses behind your analysis: study the connectivity of one single ROI with the rest of the brain, or a network of a few ROIs you have localized precisely with a preliminary study.
The functional connectivity tutorial is still a work in progress but could already help you a bit: