Are you saying you have these cells in a loop, or three of them in series ?
Assuming series, a small amount of electrons may flow for a very short while from one battery terminal to the next, but the charges will soon equalise.
There is nowhere for the electrons at either end of the cell-chain to go, so they will just stop. What you have is then the same situation as a single unconnected cell; there is nothing at the ends to discharge into.
Current is the amount of charge carriers moving per time. I=dQ/dt. As there is nothing moving, there is no current Maybe plenty of voltage, but no path so no current
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