Can I use sintered core drills without a Drill Head Assembly?

Technically, yes you can.

We don't tend to recommend it though. The reason behind the Drill Head Assembly is to keep a constant supply of water flushing the debris out of the drill hole. The sintered drills have a very soft metal matrix tip on them and if they were to get "bound up" in the glass, the chances that the tip will be destroyed are very high.

You can use a straight shank adaptor with the sintered core drills and just use them submerged in water, but it is far riskier than using a DHA for the center water delivery.