Poking around the Port of Virginia website, they largely use trucks to do any business with WV and rail for places further out that direction.
Because the inland port is just an arm of the shore port, anything going to the inland port goes through the shore port first for the most part. There is already decent road access from the shore ports to West Virginia so an improved US 48 west of Strasburg might only be beneficial to Virginia if it could be shown that shipping stuff to the inland port by rail first then putting it on a truck to go somewhere in WV is cost-effective.
The inland port says they exist to improve port access to the DC and Baltimore regions (really). About 30 companies have set up around the inland port area to take advantage of it.
I will say that even if I-73 scores better, it certainly would be cheaper to improve US 48 but in terms of what is necessary, a full fledged expressway-type road may not have to be done...just some spot improvements. Currently the truck AADT at the state line is barely 150 (6% of total traffic).
edit: fixed typo