If your not actually moving it probably not, if you were pulling them apart and you had or ended up with unconnected ic pins then maybe (as bob said).
You can protect sensitive pins with resistors or diodes to the supply rails.
Silly question.... I have some 3M magnetic tape also would that mess up anything? As a note... its for a pcb with a lcd and some chips. Including a pic and controller ic.
If all sensitive pins are connected as mentioned it'll be fine.
Also if the tape doesnt move it'll not generate static, tearing apart velcro is probably an effcient way of making static, 3m stuff will probably be fine.
I have a silicon 32 bit dev kit. ARM CORTEX4 chip, on the board the TFT touch screen is held in place with velcro, the only thing I noticed is its white not black, no idea if that makes it different to normal or not, but I am sure if this board is ok with that velcro then it should be ok with others. But I would first check that all velcro is equal.