He can travel to visit the USA while his visa is being processed. He can't enter with the intention of permanent settlement until he gets the visa in his passport. He will have to travel back to the UK for his visa interview and wait until his passport is returned to him -- a few days, usually -- before entering with the intention to settle.
For example, we made our application in August, then went to the US in September after attending the medical exam & submitting the paperwork stating we were ready to be scheduled for an interview. DH was granted entry on the VWP. He then had to fly back to the UK in January for the visa interview to get his visa. From September to January he could not work and was just in the US as a visitor.
So yes, it's possible -- just expensive and inconvenient.