Learn English – How to ask someone about the position in a waiting list

Yes, that construction is grammatical:

They are waiting for the traffic light to turn green so they can cross the street.

they can

means "they have the capability".

so they can

might be understood as referring to a result, and might be paraphrased "so they get the capability", that is, "acquire" versus simple "have".

We could say:

...so that they can then cross the street.

and draw even more attention to the fact that their ability to cross the street is the result of some condition being true.

When the light turns green they become able to cross the street. This last sentence is not how we would say it, however; it is my roundabout way of trying to make clear the sense of "contingent possibility" which is implicit in so (that).

"Is there any patient here named Ali?"
"Do you have a patient named Ali?"