The phrase "groggy with" is grammatically correct and can be used in written English.
It means to feel or appear dazed, disoriented, or lethargic due to tiredness, illness, or intoxication. Example: After a long flight, I felt groggy with jet lag. Example: The medicine made me groggy with drowsiness. Example: The boxer stumbled into the ring, groggy with the effects of his opponent's punch.
"Where?" he asked, groggy with sleep.
I was groggy with jet lag.
Groggy with lack of sleep, we started up the hill.
His knees were bent, his hands cupping the air, his eyes groggy with contentment.
"I didn't look back," said Mr. Summers, who by then was groggy with pain and exhaustion.
Players start the day groggy, with either room service or the phone book as a guide to breakfast.
She regarded her notebook with groggy dread, with loathing that her bottommost yearning right now was for yogurt.
Next morning when Scoot woke up, groggy and dazed, with a pounding headache, a taste of vomit in his mouth, and dried vomit all down his front, he'd had to admit with the cruel clarity of stone-cold sobriety: They left me here on my back to puke and choke and die, the fuckers.
There are some effective moments -- for example, an orchestral interlude depicting a drunken night that Ivan endures, wonderfully groggy music with slurpy tubas and buzzing, every-which-way counterpoint in the winds and strings.
To others, he's the guy who was sabotaged, during his first congressional campaign, in 2006, by a series of fake middle-of-the-night robo-calls, which greeted groggy voters with a recording of his voice: "Hi, this is Scott Kleeb!" (The investigation concluded this year; the calls couldn't be traced).
Getting his feet wet in a performance, Mr. Ware, the tenor saxophonist, can sound like an elephant rising to its feet: sort of groggy, not quite with the program, with some eccentricities of pitch in his burly tone.
