It possible to implement an adhoc php web application with wordpress?

What you are describing sounds like a typical CRUD app. It is certainly a possibility with WordPress (many things are), but natively it is tuned to working with content rather than forms and data. There probably will be a curve, learning to bend it for CRUD, you might not want to deal with.

From the things you named:

  • forms: WP has some elaborate forms on admin side, but very little in terms of helping you to build any. There is very little helper functionality for building forms and next to none conventions.
  • HTTP requests: WP has quite robust HTTP API for making request. However it is primarily tuned for individual requests. There is no concept of services or other ways to work with APIs as a whole, you might have encountered elsewhere with PHP (such as what Guzzle can do for example).
  • data storage and display: WP data is centered around Custom Post Types. They are quite flexible, but as above — the roots in blogging and content are showing. The thing is — it takes quite a bit of practical experience with WP to architecture data in a way that makes sense to it.

Overall my opinion is that while it is trivial for person experienced with WP to build a CRUD app in it, it probably won’t be too good of a choice for a person new to WP specifics.