Not it wont reduce the roots, only hacking at them will..
These plants should never have been used as hedges, they are TREES.
They suck moisture from all around.
Its a good time to trim it but trim it atleas 2 foot below the height you want it as it will regrow.
You can dig a trench along the line of the hedge and prune the roots as well. If you then put in a layer of weed suppressing membrane Not the thin cheapy one, a good thick one, then the roots will not be able to spread back again...not for ever, but for a good long time
Unfortunately these trees can grow at least three feet in a year which means frequent trimming. At my dads house there is one which grew into the drainpipe and up it several feet. Its too much like hard work, unless you have loads of spare time.