No it won't rebalance unless you put it back into "Auto" mode. i.e. Auto White Balance.

When you manually white-balance, you first engage Óne-push mode, and then press the 'go' button holding whatever white-card or blueish card in front of the lens. It'll hold that White balance until you reset to AWB or it's powered down for, i think, 12hours+.

It also has a couple of presets : Outdoor and Indoor.
If left on Auto, it will do the white-balance itself every time you engage into 'Tape' mode. It'll take maybe 5 or 10seconds.
Obviously also it will re-check the white-balance itself at some specific interval when it's left in AWB, and change WB accordingly.

Oh brilliant! I am going to get me a stack of coloured papers and see what happens. :)