Unfortunately, I think a lot of those heavily contaminated loads of "recycling" do end up in the trash. The only other option in many cases is for whoever manages the facility's waste to sort the good from the bad by hand, and that is generally not feasible. Some recycling centers are more strict than others about contamination, but even single-stream recycling systems won't take a load if there is more than a certain % of food, liquid, and trash. If a load of recycling is determined to be "unrecyclable" at the recycling center, it will be disposed of as trash, often at the expense of the customer (especially if the customer is a school or business that contracts directly with the recycling service). Hence environmentally-aware college students should remind their intoxicated friends to use the trash can because vomit is not recyclable (yes, I have witnessed this). In general, though, I think in the USA it's safe to assume that if the contents of the bins can be recycled, they will be recycled. Most companies won't spend money on recycling bins unless they actually plan to use them. So the answer to your question is yes, but only if you trust the American people to follow directions.

Unfortunately, I think a lot of those heavily contaminated loads of "recycling" do end up in the trash. The only other option in many cases is for whoever manages the facility's waste to sort the good from the bad by hand, and that is generally not feasible. Some recycling centers are more strict than others about contamination, but even single-stream recycling systems won't take a load if there is more than a certain % of food, liquid, and trash. If a load of recycling is determined to be "unrecyclable" at the recycling center, it will be disposed of as trash, often at the expense of the customer (especially if the customer is a school or business that contracts directly with the recycling service). Hence environmentally-aware college students should remind their intoxicated friends to use the trash can because vomit is not recyclable (yes, I have witnessed this). In general, though, I think in the USA it's safe to assume that if the contents of the bins can be recycled, they will be recycled. Most companies won't spend money on recycling bins unless they actually plan to use them. So the answer to your question is yes, but only if you trust the American people to follow directions.

Sources:

Waste Management sends food-contaminated materials to the landfill. The page linked explains the effect of grease and oils on paper recycling, and exploration of the site confirmed that WM sends food-contaminated plastics to the landfill. The site also indicates that food impacts aluminum foil recycling.

As another example of how impurities effect recycling, Pacific Steel & Recycling in Havre, MT has very strict guidelines about sorting papers and cardboard because mixed newsprint/office paper bales are worth much less than pure newsprint or office paper, transport costs are high, and recycling volume is low in a rural town of ~9600 (source: conversation with an employee). And those are impurities that don't completely ruin the material for recycling the way food does.

As alluded to above, recycling companies make a profit by turning waste items into raw materials for manufacturing. So as long as what they receive isn't too badly contaminated, they do recycle it. If a business contracts with a recycling company for on-site pick-up, you can be sure that uncontaminated loads will be recycled.