I admire your ambitions and drive in the field. Very commendable.
It depends on your academic area, I suppose. This would be impossible in my field (biomedical sciences). Without extramural funding it's almost impossible to conduct research, especially given the need for lab space that a university would supply (not counting the supplies, access to data sets, etc...).
Keep up the great work. Hope you land the tenure-track position in the future that you definitely deserve.