It looks like 'grazing rye is secale cereale just like rye the grain crop (see
https://www.cotswoldseeds.com/articles/718/sowing-and-growing-grazing-forage-rye) for example. It may be the variety you have won't be optimised for grain size but leaf growth, but ought to form heads just the same. According to wikipedia it can be annual or biennial (maybe dependent on sowing time?) You could probably sow it now or in the spring to crop next year. It ought to die after cropping, so not be a persistent weed unlike
ryegrass (lolium perenne) which is a perennial grass. Even if it does seed around the only problem is that you won't be able to tell easily whether the grass is rye or a less useful grass.
I was very pleased with the harvest I got from the handful of seed or rye I was given this year, but those are from 'fulltopt'. Sown in spring they produced a nice crop in August for me. If you like I can probaby send you a few seeds to play with and compare to the grazing rye....