When a cell is connected to full load does it drop some of its voltage due to internal resistance and quickly jumps back to normal whenever the load is taken off??
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Yes, that's the basic effect of the ESR (equivalent series resistance) and the capacitance of the cell.
If you use any free circuit simulator and play around with reasonable values of R and C, you will get a better understanding of what's going on inside the cell. If you measure the given voltage drop with a known current and the time taken to recover, you can derive the correct values of Rs, Rp and Cp in the example below.
