After Drupal 7.32 should sql injection attempts create PDOExceptions?
It is my understanding that in theory, yes, a compromised site from the particular vulnerability could lead to such behaviour. As Drupal.org recommends, in such cases you should treat your site as compromised and all next actions should be the appropriate for this case.

The fact that you patched the site shortly after the announcement, as you mentioned, is very important. As far as I have seen, most attacks are coming from scripts and it has not come to my attention any automated attack that would cause such behaviour (to my experience of course). This again is not reassuring, just a thought on the possibility for the nasty thing to have happened.

Apart from the obvious actions (see links below), I would definititely take a good look of the code that doesn't behave nicely. Also a good tool is always diff comparing to clean code. I would as well take a good look in the db. Last, there might also be a possibility that some contributed module has got issues with 7.32 or maybe anything else that might have been updated.

Drupal SA-CORE-2014-005 - How to tell if my server / sites were compromised?

https://www.drupal.org/drupalsa05FAQ