"may hardly" is correct and usable in written English.
You can use it when you want to express that something is unlikely to happen. For example, "We may hardly make it on time for the beginning of the show."
It may hardly be sour at all.
above the new speed, a difference the driver may hardly register?
Sadly, given the success of imports, consumers may hardly notice if one or more companies disappear.
In Turkey, Recep Tayyip Erdoğan's inability to take a joke may hardly be news.
In the evolution of ideas, the day's importance may hardly be noticed at the time.
But you may hardly remember that tournament's regional semifinals and finals, the games over the second long weekend.
She encouraged Starbucks to open a shop in Fargo last June.Starbucks may hardly be the apex of hipness.
Workers for different companies may hardly know one another despite working side by side; they often answer to different bosses.
To casual Web surfers, it may hardly feel that the Internet has been trapped in an intellectual vise grip.
Clark himself may hardly be dancing now, but we remember exactly why we used to go to all his shows.
Some polls warn he may hardly have more than a people-carrier full of MPs after the next election.
