In the programming biz, they often will if you've got a track record to back it up. Contributing to open source projects is a route to getting such a track record.
If you already have a degree, just in the wrong field, you don't need to get another degree. Just get the training by whatever means.
Heck, my degree is in mechanical engineering, yet I had jobs writing software.
In my own experience a track record is meaning less and less, and employers are really starting to fixate on credentials. It's very weird and disconcerting to a fellow like myself who likes to believe an impressive record should speak for itself. But apparently it's not speaking as loudly as it used to.
There really is a "cult of the degree" and I really don't get it. Is the field getting saturated and employers are finding it necessary to erect barriers? Does this, an average, make good fiscal sense? I would think successful, relevant experience is something (that when verified) would reduce risk for businesses.