Yes, I did it this year. A bushog can work, but it will depend on the bushog design type - prefererably one that kicks the grass out rather well without shredding it up into little pieces. My old square back bushog accomplishes this quite well. There are also rotary cutters made where one side unbolts called a "hayside" for use with hay. Additionally many farmers have modifed their own cutter by cutting one of the sides off.
As for drying times: Compared to a haybine/moco it will not be quite as good, but it will dry much quicker than a sickle cutter alone. It will serve kinda like a "poor man's haybine" as the stems are cracked some. It will not affect Nutrion in grass hay at all, but in alfalfa it could if you experience leaf loss - I would not use in alfalfa unless desparate.
The bad news: I can not speak from experience yet (hope to have my old sickle going this year), but everything I have read suggests you will lose some yield using the rotary cutter (others estimations are 20%-40% loss). Or in other words, if you are getting 100 bales per acer now you may only get between 60-80 bales per acre as some will be left in the field.
I myself am hoping to try the sickle for increased yields, but I will continue to use my old bushog on those occasions when I must have the benefit of faster dry down times due to the "poor man's haybine" effect.
Lastly, search this site and "Yesterday's tractor" as this topic has been covered extensively. You will read both success stories and horror stories. In my opinion the horror stories stem from people using the wrong rotary cutter. Lastly if you have not already purchased your rotary cutter consider purchasing one of the "hayside" models from King Kutter if you are looking at new units. Same pirice as their standard model with increased flexibility (TSC will have to order it though).