"I've heard that the clothing type Tyvek fabric is by itself only somewhat highly water resistant (whereas the Homewrap is noticeably more so), wouldn't it be a good idea to coat it with some kind of DWR type repellent? Or would it still just wet out anyways if in an extended downpour?"
Wind shirts normally have zero hydrostatic head and only can be considered water repellent. Tyvek has some hydrostatic head. For 1443R Tyvek the Hydrostatic head is 850mm. Some tyvek versions have more than 3,000mm hydrostatic head. Tue DuPont TY127S Disposable suit mentioned above has a hydrostatic head or 1,000mm according to a quick google search. Most water proof fabrics have a hydrostatic head of 17,000mm or more.
So in a rain storm that would cause a wind shirt to completely soak through in a minute, tyvek can still keep you dry. Only in very heavy rain will a limited amount of water get through tyvek. If a fabric has some hydrostatic head mosquitoes cannot bite through.
Please note there are versions of tyvek that are pin perforated. Pin perforated Tyvek, like a wind shirt, also has no hydrostatic head.
Also Tyvek is made from Polyethylene plastic which is inherently DWR. There is no need to add a wash in DWR to tyvek. Besides wash in DWR coatings will not add any hydrostatic head to any fabric.
If the forecast is 100% chance of rain and I had a choice of Tyvek and a wind shirt, I would take the Tyvek.