does 0,7V supply on 5V devices damage the device?
Yes and no.

The supply voltage itself shouldn't cause any damage, no.  However, any signals being fed into the chips which are greater than 0.7V could cause damage.

For instance, many chips have input values listed in their datasheets as "\$V_{DD}+0.3V\$", which means that for chips like those, any voltage greater than 1V applied to its input pin when being powered from 0.7V will be out of specification and likely to cause damage.

So check the datasheets for your chips, and your circuit, to make sure that you're not going to fall foul of that.