Can creators of applications for the web use Web Applications as a Q&A resource for their own creations?
What's the general feeling?
Would this be welcome?
Maybe it's the done thing already and I just haven't seen any!
There's nothing wrong with you answering questions posted here about your web application as long as you've made it clear who you are in your profile.
There's no need to declare your affiliation in each answer as the question referencing your application already exists. See this Meta Stack Overflow question on Facebook employees answering questions.
However, I'd be wary about trying to use the site as your main support resource. Synergy tried this with Super User and it didn't end well. People came to the site not realising it was a general* Q&A site and this caused issues with the quality of the questions asked.
If you were to answer a general question with an answer that publicised your application - as long as the answer was relevant - then you must declare your affiliation in the answer.
* within the scope of the FAQ of course.