I doubt it. I can't say for sure... some of that "smart blocker" type stuff, or the "Arrow DT White" might work but something tells me this would be a large bit of awning cloth that is not easy to situate in a heat press.
Can I suggest you explain the exact specs of the job (lettering only? single color? custom, match or standard color... printed fades or images, or just one solid color... now big of image or text... how much copy? what color sunbrella? sewn, unsewn... stretched over awning frame already, god forbid?...)
I've screenprinted dozens of awnings, but I've also hand painted along pounce pattern lines & also painted over vinyl mask.. so there may be some other helpful suggestions that could be relevant based on job specifics. I don't know if this would be of interest, but I only just discovered the other day that Glen Raven offers inkjet receptive Sunbrella, so I will be printing on some of that soon.