Is "go to the hospital" used even when referring to multiple hospitals? [AmE]

Solution 1:

Yes, in American English

go to the hospital

means to go to a generic hospital. There is no need for a specific hospital to have been mentioned previously in the conversation or for there to be a single assumed hospital in the area which is the only one.

In the phrase

... sending hundreds of people to the hospital by the afternoon.

those people could have gone to many different hospitals - it is not implied at all that they are all at a single hospital. Only real world knowledge would help figure that out, like whether they are in a community with a single hospital or a one with more than one hospital.

Solution 2:

This begs the question--whether Americans use the phrase to the hospital even when people go to or are sent to multiple hospitals.

To say "yes" to this question might erroneously tell you that Americans don't know how to express the idea of going to multiple hospitals or sending people to multiple hospitals. That is not the case.

As you have correctly guessed, American English speakers can ignore the idea of multiple hospitals by using the phrase to the hospital only when they find it unnecessary to convey the idea, just as British English speakers can by using the phrase to hospital. When they find it necessary to convey the idea of multiple hospitals, however, both American and British English speakers would choose to use the plural form hospitals.

For example:

Two US Capitol Police officers were taken to different hospitals, Pittman added. with injuries and one died [from CNN]

And data from the UK's Intensive Care National Audit and Research Centre (ICNARC) shows almost three times more patients than usual were moved to different hospitals - sometimes hundreds of miles away from their home. [from BBC]

Solution 3:

Interesting question. As a native speaker of midwestern US English, I think

"sending hundreds of people to the hospital"

is acceptable but (imho) very slightly awkward, exactly because of what you pointed out about them surely going to many hospitals.

"sending hundreds of people to hospital"

would be unlikely here, and sound specifically British.

"sending hundreds of people to hospitals"

would be likely, and sounds best to me. Newspapers often write "to area hospitals" or "to nearby hospitals".

Your analogy to "to school" and "to church" suggests there is a distinction in play between an institution per se, and a specific instance (commonly associated with a particular building) -- the latter sense fits well with using the definite article; the former, not so much.