Always is in PDB that time of year. Well - as you know in August it was impossible to get a pre-booked room anywhere last minute at a sensible price (under 150Euros) and I didn't bother, opting to live out of a hire car for 3-4 days instead. Which was interesting
but not that different to most trips in the end where the pre-paid hotel room was rarely seen and sometimes not even checked into. Rest of the year if I pay more than 45Euros a night in San An for a decent shower and laptop charging plug I think I've been sqeuuzed lol. Getting affordable single rooms anywhere decent is obviously much harder than if there are two of you.
Straight answer is usually they are cheaper at the last minute, yes, as long as you are flexible about where you stay and with a bit of luck. From memory about 60% off regular rates at Gran Sol in June for a couple of nights mid-week for example. I don't usually go out in early to mid-September for various reasons but last minute prices typically more than June/July and less than August - both for flights and rooms over recent years.
If you have a car it's no bother to move if you need to over a few days too. Otherwise more of a faff. I rarely book an Ibiza trip at more than 2 days' notice and so it's always last minute or nowt. Forget PDB as a single traveller in most of September too, especially for a sensibly priced room. If you have a car San An is only 1/2 an hour away. Otherwise if you want to go out on the South side of the island every night the taxi companies will likely rob all you save in cheaper accommodation staying in San An, so unless you have a friend with a spare seat it's bum around on buses or cough up - one way or another you'll likely wind up handing the dosh to someone !