It probably depends on the thickness of the steak, and how well you like your steak cooked.
I know I can cook frozen burgers about maybe 2cm / 0.75 inch thick in a double sided grill (George Foreman or similar), and it'll come out to a doneness that I like.
If you prefer your steak more towards the rare side, and it's not multiple inches thick, I'd think you'd be okay ... it won't be as good as something that you let get to room temperature before cooking, but it won't be bad.
If it's still not done well enough to your liking once the outside's gotten a little bit of char on it, you can put it in a warm oven to cook through 'til it's to the doneness you prefer.
I would think that USDA would err on the side of conservative when it comes to safety, especially with no financial interests in the equation
http://www.fsis.usda.gov/Fact_Sheets/Big_Thaw/
Perishable foods should never be thawed on the counter, or in hot
water and must not be left at room temperature for more than two
hours.
Even though the center of the package may still be frozen as it thaws
on the counter, the outer layer of the food could be in the "Danger
Zone," between 40 and 140 °F — temperatures where bacteria multiply
rapidly.
When thawing frozen food, it's best to plan ahead and thaw in the
refrigerator where it will remain at a safe, constant temperature — at
40 °F or below.
There are three safe ways to thaw food: in the refrigerator, in cold
water, and in the microwave.
They're all covered in the above link, but here's the fastest one since it best meets your requirement of reasonably quick results:
Microwave thawing
When thawing food in a microwave, plan to cook it
immediately after thawing because some areas of the food may become
warm and begin to cook during the thawing process (bringing the food
to "Danger Zone" temperatures). Holding partially cooked food is not
recommended because any bacteria present wouldn't have been destroyed
and, indeed, the food may have reached optimal temperatures for
bacteria to grow.
After thawing in the microwave, always cook immediately after, whether
microwave cooking, by conventional oven, or grilling.
Foods thawed in the microwave should be cooked before refreezing.
And when all else fails:
Cooking without thawing
When there is not enough time to thaw frozen
foods, or you're simply in a hurry, just remember: it is safe to cook
foods from the frozen state. The cooking will take approximately 50%
longer than the recommended time for fully thawed or fresh meat and
poultry.
From personal experience, I prefer the cold water method to microwave for fast thawing, but I rarely if ever use a microwave anyway so others on here might have techniques that minimize the flavor/quality downside of it.
The factors that make the microwave method less safe are what also lower the quality, taste and texture of the food – the unevenly thawed parts, over-cooking some of it while undercooking other areas, etc.
Best Answer
For short term freezing they should be just fine as far as texture and taste are concerned. Just make sure you avoid freezer burn by wrapping them tightly in plastic wrap and then either aluminum foil or a freezer bag. If you store them more than a few months then they will start to degrade.