I've seen a few very old cues made from white oak. There should be no problem, per se. Oak is a very strong and stable wood. Both species are not horribly far off of hard maple in density.
The problem with oak is that it will look like you went to a house and cut balusters out of a staircase and made cues from them. Oak is not an attractive wood and has wide-open pores. Finishing to anything near what a cuemaker should be aiming for will not be easy. Oak also tends to shatter out when working.
I have used cherry and walnut in cues, so you don't have to buy a $200 piece of burl to start. There are 'exotic' species that are affordable and interesting. Things like purpleheart, sapele, canarywood, etc. work well and look the part.