I really don't see why they shouldn't. After all, it could be argued that whether Mr Motion was an establishment poet or not, he became one as soon as he got that call. But this would be too facile a view. It depends what is meant by "Establishment".
Henry Fairlie's definition of 1955 is the one now generally cited: "I do not mean only the centres of official power," he wrote in the Spectator, "though they are certainly part of it, but rather the whole matrix of official and social relations within which power is exercised." Before that the Establishment had been roughly confined to the Church, then the judiciary, the Lords and the Commons, but by the 1950s this obviously wouldn't do, since fewer and fewer people cared what bishops said, and it had long ceased to be obligatory to touch a forelock to the squire. But I'm not sure that the Fairlie definition is much help either.
The Establishment, as defined by Fairlie, now includes anyone who has an influence on the way other people think. The adjective establishment is often used as though it were rather a dirty word, which made good sense so long as everyone who was thought to belong to the Establishment had the same ideas on life, which they proceeded to dictate to the rest of us. This is no longer so.
It's not a tightly-knit body anymore. It includes pop stars, media moguls, supermodels, captains of industry, football managers, television personalities, transplant surgeons, self-appointed arbiters of taste, and spin-doctors of various stripes - a pretty heterogeneous bunch. The only thing they have in common is that they might all at one time or another expect invitations to No 10. Establishment with a capital "E" means very little. The matrix has broken up.
For the same reason, the adjective has lost any precision it might once have had. I suspect that when most people say it they merely mean "orthodox". You might even say that it's done an about-turn. The principal objection to Mr Motion, so far as one could gather, was that he was too ready to go along with received ideas, not that he imposed them on others as the old Establishment did. Some people use it as a slightly grander alternative to "fuddy-duddy," and this certainly accords with the earliest sense of the word, which simply meant the act of making - or the state of being - stable, which in turn came from the Latin stare, to stand, implying resistance to change. An established man was someone who was settled in life. Whatever we may think of Mr Motion, he is clearly an established poet, with or without the laurels.