She was likely not a full-time teacher
Rolanda Hooch doesn’t appear much in the books (even less in the films) and there is no proper Pottermore article on her (only a characters-from-the-films page, which isn’t by Rowling), so there is—to my knowledge—no canon information to answer this decisively. The way I’ve always read things in my head, however, matches what dunraven’s comment above says, that she was probably not a permanent, full-time teacher at Hogwarts.
There are a few things that hint at this, though only circumstantially:
1. Her age might indicate retirement
If we accept the Philosopher’s Stone video game (sorry, Wiki link) as canon, then Rolanda Hooch’s broom was singed during the Great War (i.e., the First World War). Presuming that she had left Hogwarts before she had anything to do with the War, she would have been born no later than 1900, making her at least 90 years old at the time of the Harry Potter books. (The fact that she falls asleep during one of the Quidditch practice sessions that she oversees may be an indicator of somewhat advanced age.)
As such, it would seem plausible that she has retired from any actual, full-time teaching career she may have had (whatever she may have taught), and is now more loosely connected to Hogwarts, coming in to teach flying lessons to first-years and oversee various other broom-related events, such as Quidditch training and matches, when called for. If she lives in Hogsmeade, this should be fairly easy to arrange even on short notice. In fact, as pointed out in the comments, it should be fairly easy to arrange even if she doesn’t live in Hogsmeade: she could easily apparate from more or less anywhere in the country to Hogsmeade and walk the short distance from there into the school grounds. Communication doesn’t seem to be an issue either: both owls and Floo network communication seem to work very well (when Umbridge isn’t Headmaster, that is).
There’s also nothing in the parts quoted in the question here that goes against this: McGonagall only says, “I’ll ask Madam Hooch to oversee your training sessions”, which would still be perfectly logical if Madam Hooch was in frequent communication with the school and on call to come by for such things.
2. She’s never referred to as Professor
We know that she has an office at Hogwarts,1 so I would say she must be considered a member of staff (though having an office doesn’t necessarily make her a full-time member of staff, of course). To a certain degree, the students probably also think of her as ‘one of the teachers’. But it is notable that she is consistently referred to as Madam Hooch, never Professor Hooch.
The title Madam seems to be a fairly generic term of respect towards witches in general in the Potterverse: it is used with various witches like Madam Rosmerta and Madam (Amelia) Bones, for example. It is also, importantly, used for the only other two non-teaching female members of staff at Hogwarts we know of: Madam Pince the librarian, and Madam Pomfrey the healer. (I don’t quite consider Mrs Norris staff.)
All the members of staff that teach, however, are consistently referred to as Professor, regardless of gender: Professor McGonagall, Professor Flitwick, Professor Snape, Professor Marchbanks, Professor Trelawney, etc. The only exception to this is Firenze and, well, he’s a centaur. During the first class with him, we even see that Parvati Patil seems rather unsure of what to call him:
“Please – er – sir –” said Parvati breathlessly
Order of the Phoenix, ch. 27: “The Centaur and the Sneak”
3. Her general absence
Finally, there is the simple fact that, apart from the flying lessons and the Quidditch training/matches where she appears, we never see Madam Hooch at all in the books. All the other teachers that play an actual part in the book make random little appearances throughout, showing that even if there aren’t any actual scenes with them, they’re still around. But no one ever runs into Madam Hooch in the hallway or anything like that, and even when something happens that involves most of the teachers in one way or another (like Fred and George spreading mayhem before flying off, at which point we see Flitwick wondering if he has the authority, McGonagall telling Peeves a chandelier unscrews the other way, etc.), she is absent.2
The only other teacher in a somewhat similar situation would be Professor Trelawney, who never shows up outside her own rather limited teaching schedule either (except for a few select scenes: her near-sacking, the Christmas lunch, her sherry-hiding foray, and of course the Battle of Hogwarts—where Madam Hooch is also absent, incidentally). Unlike Madam Hooch, though, who is very much an outdoorsy person and would likely to bonkers if she had to stay cooped up inside a castle (not to mention an office in a castle) all the time, Professor Trelawney is more than happy to remain in her solitarily stifling tower chambers fiddling with her crystal ball and sherry bottles, so there’s less to wonder about there, and her nigh-complete absence is easier to explain than Madam Hooch’s would be.
The fact that Madam Hooch is absent from pretty much everything but her actual (conjectured) teaching duties is a good indication that she simply isn’t there the rest of the time.
1 From Chamber of Secrets, ch. 10 ‘The Rogue Bludger’: “But the Bludgers have been locked in Madam Hooch’s office since our last practice, and there was nothing wrong with them then …’ said Wood, anxiously.”
2 Even at the Start of Term Feast in Philosopher’s Stone where Dumbledore says that students wishing to try out for Quidditch teams should contact Madam Hooch, she is never mentioned as being present, though it’s possible she was.
