Is it inappropriate to email a senior academic with whom I have no pre-existing relationship, asking to check/inform my work?
Inappropriate or not, you aren't likely to get a response. Professors tend to receive a lot of email. If they don't have a compelling reason to respond, they might not.

You're asking them to put time and thought into a response to a stranger. The best course would be to talk in person to a professor whose class you've taken. Ask if they would mind looking over your work, and get feedback in person.