No, it was entered into the holothurid mouth by chance.

I may be wrong because have not seen a lot of echiurids, but the white semitransparent creature on your picture resemble me Holothuroidea Chiridota I met at the White Sea.  

or this may be a juvenile sipunculid; it cannot be seen clearly, but its cuticle seems to have some thorns; the tentacles also look more like those of sipunculids

I think it is Priapulida (Priapulus caudatus) 

http://mek.oszk.hu/03400/03408/html/2970.html

to distinguish between these you have to look if these tentacles are really tentacles (then it's a sipunculid) or the caudal appendages (the "tail" of Priapulus); and also for the cuticle structure (if there are only papillae or also chitin thorns characteristic of sipunculids).

To argue for holothuroidea version - pay attention on the white round spots - they resemble the groups of spicules of Chiridota (you know that echinodermata contain CaCO3 spicules inside the skin). And the crown of something looks like ambulacraria system. And the posterior(?) part of the animal brings rings of contraction - you see such features during dissection not so well relaxed Chiridota. As far as I remember  Chiridota feeds on sediment, so may be polychaeta attacked and tried to beat.

Any reason why this is not simply an anemone eating a polychaete, as they commonly do? [check basic internal anatomy to confirm phylum; check 'tentacles' for presence of nematocysts]

I am adding another pic of the same specimen ..may be it helps 

Some polychaete enter the gastric cavity of holothurians, that it could do for protection

It's an anemone.  There are too many muscle bands for it to be a holothuroid and the dermal bumps appear to be papillae rather than ossicles.

Yes, the second picture looks like Anthozoa for me, not holothurioidea Chiridota