I'm not an authority, but from what I've seen on these forums, if you host your own instance on your computer and are savvy with scripting languages, you can do that and almost anything else.
If you use the cloud-hosted solution, however, you can't make that kind of customization.
Jim is right - you'd want a listener to pick up "issue edited" and transition the issue through the right transition. Which you can't add to Cloud
What you could do is reverse it - have a workflow transition that sets the assignee to current-user, so when a user says "move to in progress", they don't have to think about assigning it to themselves.
Listeners are global things, so your code would probably need to have "if project = X and issuetype = Y" type stuff in it (unless you really wanted this globally)
I'd use the script-runner to do this, but the other main (free) option is to write your own add-on to provide the function. (Bear in mind what Jim said - this is server only)
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