Bowmasters + Horntail?

So let's say that I never HP washed but wear HP equipment, enough to HT for the heads, not the whole body. Can I just stay at the heads area and continue to cast SE for the party while they attack and I eventually get a Pendant + Egg? Let's say in that situation I didn't have any connections, is it likely?

You're in Bera, right?

Not only is the situation you described unlikely, it's impossible. What good would you be if you could only SE for the prelim heads? No group would be that desperate for someone. And either I misread what you said or you don't fully understand how HT works. The prelim head maps are two different maps, both separate from the main room (where HT itself spawns). You can't stay in them and still SE your parties. Once you enter the main room, there's no going back to the prelim head maps.

Regardless, even if you partially washed + HP gear, it's very unlikely you'd find a group in Bera desperate enough to take you (assuming you have no connections that'll give you easy access or something). The only way you're gonna get in is if your character has good HP, you're reliable, skilled at surviving the battle and very patient for a group to even take you once. It can be hard to get established in a group, but if your character is high leveled and good at surviving, you'll get in eventually.

Don't expect to be like those stupid bowman who uber wash and then ride on their connections to get into groups. Groups don't need weak "SE mules" all that often, especially in the main servers.