It is scalable. It scales linearly (and for practical purposes indefinitely) with the amount of money you spend on AWS Lambda. It might not have a nice constant factor, but it is scalable.
This is just pedantic. Anything can be scalable using that definition. Heck, I could hire a 3rd world worker to manually draw the PDF's, scan them to PDF using a scanner, and put them on a server and it would "scale linearly with the amount of money I spend" on labor.
No, some things can't be, like badly architected monoliths, or databases. Especially with databases it's not a given, which is why for quite some time in the last years things like the "MongoDB is web scale" blew up and people started mindlessly asking "is it scalable" (which as you figured out, means very little for a lot of systems). I'm also pretty sure that your example scales worse than linearly, since you have to introduce multiple levels of management at some point.
"scalable" = "can it be scaled", which is not a given for every system
Redrawing the PDF's and scanning them would likely not scale linearly with the amount of money you spend on labor. Labor tends to have diminishing marginal returns. The cost of hiring two workers is more than double that of hiring one worker because there is additional complexity in coordinating the workers.
Also, for the record, this comment I'm making right now is just pedantic.
If there is only one worker the requests can flow directly to that one worker. If there are two workers, something would need to sit in the middle and determine how to distribute the requests. That extra hop is where the extra complexity comes from.
