I’d say yes, personally, but the rules explicitly say it may be challenging for a low level PC to run their own domain (p134)
Things to consider:
Below Name Level (9th) a PC will not attract followers, so any guards, etc… will need to be hired as Mercenaries or Specialists and paid for - which could prove expensive.
Nor will a PC automatically gain any peasant families, but they can spend money to attract them. Again, expensive.
Unless the Vassal Domain/Realm has an existing Stronghold for the PC to use, they will have to build it themselves which may be prohibitively expensive for lower level PCs.
The size of the stronghold will also limit the peasant population of the domain.
It is generally assumed that a PC will be a vassal to a higher power at 9th level (P131), so it is perfectly reasonable to assume lower level PCs will be so as well…
P134 says swearing fealty to a higher level NPC lord is a good idea, as a lower level PC - so your L1-6 guys could be vassals, yes.
That’s what the rules say… For my own opinion,
Any PC is eligible to run the holdings of a higher level NPC. However, whether a PC has a stable enough income and is powerful enough to defend the holding may be limiting factors.
It puts a different slant onto the game in my mind. PCs are adventurers - that is, they go out and make stuff happen, make a name for themselves and get rich. Tying them to a domain makes the game feel ‘smaller’ to me, and more like Ars Magica than D&D.
It’s a neat idea, and definitely one worthy of exploration, but make sure the PCs have enough freedom to have adventures as well as tend to the Domain.
I’d be interested in reading your experiences if you go down this road.