In various forms, yes.

Edward Stafford would not have been as personally involved however. The series alludes to his estates and the power therein, and that was the focus of his attention and of tension. He also exercised control as one of the Wardens of the Welsh Marches. His main position at court was a member of the King's Council, and he was not a particularly frequent attendant because he did not have a strong enough advisory relationship with the King to feel worth it. In contrast, his emphasis on his ducal and regional power was the cause of suspicion. The one time Stafford was a personal attendant was in a more prestigious but temporary ceremonial position as Lord High Constable and Lord High Steward at Henry's coronation.

In contrast the characters of William Compton, Anthony Knivert and Charles Brandon were actually attendants in the King's Household. According to his biographer, S. J. Gunn: "By about 1503 Charles Brandon waited on Henry VII at table and by 1507 he was an esquire for the body. More excitingly, by 1505–6 he was one of the company of king's spears, martial young gallants active in jousts and courtly display." You can see that he did attend him at the table, similarly to the way Buckingham (probably inaccurately) is portrayed as doing. The eventual Duke of Suffolk also held the adjunct position of Master of the Horse, which had a sort of department under them (see for example "Ritualistic Equestrianism: Status, Identity, and Symbolism in Tudor Coronation Ceremonies" by Keri Blair, 2020). This position was important because it solidified his status in Henry's sporting activities as his leading co-player, gave influence over travel arrangements and the primary right to help the King off his horse. William Compton was Groom of the Stool and Chief Gentleman of the Bedchamber, which made him extremely important in the personal life of the King. The Groom of the Stool, it must be said, was prestigious because they were the one who assisted the King while he went to the loo. Personal attendance in this way, while seemingly servile, would have been done almost ceremonially and it allowed great access which could be turned into influence. Anthony Knivert is based on Thomas Knyvett (not sure why the name change) who was also a jousting participant like the others, and was Brandon's predecessor as Master of the Horse before he died in a sailing accident in 1512.

These men are not high nobles, which is typical. The chamber attendants were usually at least half from gentry, and many of the most important were not actually nobles and used their access to rise which was a cause of resentment (people like Suffolk). Nobles serving in the chambers usually were the untitled relatives, daughters from nobles and gentry often served briefly as Maids of Honour before their marriage. Most adult titled nobles were after more typical positions, and those involved in the chambers were usually angling for the high leaderly positions like Master of the Horse, Lord Chamberlain or Captain of the Gentleman-Pensioners. High-ranking women though, seem to have been more likely to stick with this service, which makes sense given they couldn't serve in any of the offices. A number of Elizabeth I's important ministers had wives in the chamber, for example Catherine Howard, Countess of Nottingham and Mildred Cecil, Lady Burghley. The Bedchamber was the goal if you wanted to capitalise on it because it was more intimate, and positions like Groom of the Stool and Chief Lady of the Bedchamber in counterpart to Compton would be the feminine ambition, and the only leadership offices women could be appointed to. Elizabeth's ladies of the Bedchamber, however in return for their position had the rather Herculean task of dressing the Queen in the morning which could take hours (!!). They were the only people allowed to see what she looked like without all her trappings.

It's really important to understand the politics of access that went into this. In the Medieval period and increasingly so in the Early Modern personal access to the monarch was one of the main paths to power. Henry VII established the formalisation and expansion of the Privy Chamber, the Bedchamber began to develop in Henry's time and became more from the Privy Chamber in James I's reign. While the Privy Chamber was mostly ceremonial and officious, the Bedchamber was largely personal and physically intimate; albeit in a somewhat ceremonial and officious way (see for example “Bedchamber Ritual and the Performance of Stability in Jacobean England, 1603-1625”, Jennifer Shun-Yee Ng, 2011). The hierarchy of attendants from more lowly servants to intimates is determined by the perceived significance of the task The most important positions of access would not have been particularly strenuous physical labourers, more low-ranking attendants would done more of the hard work and had more demanding expectations. But people who did seemingly menial though intimate tasks for monarchs were influential, and they were expected to be on hand whenever required. So there is a kind of political, glorified servitude. But it was more important that is depicted with Buckingham, who probably would not have done such things.