It all depends on if there were any architectural changes to the parts of the OS that HDP interacts with. You can try installing it and testing it out to know for sure, but I would imagine it is possible. I have not tried it myself nor would I recommend it until it is certified.
As per https://supportmatrix.hortonworks.com/ the Ubuntu 18:04 is not tested and certified by Hortonworks QE team for using with HDP. but i see as Ubuntu 16:04 is certified their won't be any issue with using 18.04.
Have a look on the python version and jdk version and see if its in supported list.