Bypassing battery cell with transistors
Yes - it is entirely "doable".
A transistor "works" regardless of external applied collector or drain  voltage - but you can see that it is working externally only by applying voltage.

Be CERTAIN that S1 and S2 are NEVER both on simultaneously :-) :-( !.

You could use a bipolar or field effect transistor for both locations, but a FET is liable to be easier to use overall.  The FET needs adequate Vds rating - say 20V or more, and a current rating at least a few times higher than expected peak current.

Connect a say 100k resistor from gate to source in each case. To operate connect V+ via a resistor (or even directly) to one or other gate - BUT NEVER both at once.  

Most FETs will tolerate 8 or more volts from gate to source. Ensure that yours does.

How much current do you wish to draw?