No, it doesn't even make sense for him to awaken it.
The whole point of the fruit is that it's incredibly destructive and reckless, and Whitebeard is the opposite of that.
Most times we saw him making a decision it was calculated and well thought out.
Only time he did something that was a little reckless and brash was him going to Marineford, but even then he literally intended to die there while saving Ace.
Basically he didn't have the personality fit for the fruit, that's why BB will be the one to awaken it.