Yes, if I am reading your post correctly it is possible.
The Alteryx Server has a REST API but it may need to be switched on to use it. If it is switched on you should be able to get an API Key and Secret from the Keys section of the Account page.
You can then use the API to get a workflow, get the questions then run it and finally poll its status and then fetch its output.
The sequence would be something like:
1. GET a list of all the workflows from /v1/workflows/subscription/
2. For the specific workflow get the id the call GET /v1/workflows/{appId}/questions/. This will give you a JSON structure of questions
3. Build a set of answers to the questions in JSON and POST to /v1/workflows/{appId}/jobs/. This will queue the job and return a job id
4. Poll the job status by calling /v1/jobs/{jobId}/ and wait for completion of failure
5. You can then finally call /v1/jobs/{jobId}/output/{outputId}/ to retrieve the output
Documentation and sample C# and JS applications are on https://gallery.alteryx.com/api-docs/
Hope it is enough to get you started