Mark
Not necessarily. HEPA Cloth bags are usually rated for the HEPA H11 Filtration Standard. And that's for most OEM bags with the vacuum manufacturer's name on it. Generic HEPA Cloth bags work well too, but aren't quite as efficient. If you look at VacLab's tests on YouTube of the Clean Fairy brand Kirby HEPA Cloth bags vs the OEM Kirby HEPA Cloth bags, that illustrates it well the difference in filtration between OEM and generic.
I think HEPA H11 is most efficient in capturing particles down to 1.0 micron if I remember correctly? Whereas HEPA H12, non washable HEPA filters, and HEPA H13, washable HEPA filters, filter down to 0.3 microns according to the EN1822 standard. HEPA H15 is the latest revision to the EN1822 standard, rated to capture down to 0.1 microns. ULPA Filters, such as offered by Nilfisk and Fakir, also capture particles down to 0.1 microns. So while your OEM HEPA Cloth bags will capture most large and fine dust particulate, it will not capture ultra-fine particulate such as bacteria, smoke and odour particles. That's why most vac shops and manufacturers recommend the use of a vacuum with a HEPA Cloth bag and a HEPA Filter in a sealed system for allergy sufferers.
About older vacuums - What Alex, Vacuumdevil, means is that ya sure you can add a HEPA Cloth bag to a older vacuum, BUT the vacuum itself may not be entirely sealed before the bag. A Hoover Elite is a perfect example....you can put a HEPA Cloth A bag in with a gasket on the bag, but the tube that carries the dirty air up into the bag, where it attaches to the motor isn't perfectly sealed. So yes the air will be cleaner for sure, but you won't be getting the best possible results if the entire air path before the bag isn't entirely sealed, and if you can you should make a effort to seal it up first before adding a HEPA Cloth bag. This is mainly a problem for older direct air vacuums, though, not clean air uprights and canisters.
If somebody comes to me looking for a recommendation for a sealed HEPA vacuum for allergy sufferers, or they are looking to buy one from me and they mention they have allergies, I first find out what vacuum they have, it's condition and if it can be repaired. If it is in good shape or repairs done for reasonable cost, I always suggest to people to first try using a HEPA Cloth bag in their vacuum and see if that helps with their allergies. Then if it doesn't, then they can go ahead and buy a sealed HEPA vacuum with a HEPA Filter on the exhaust and sell the old one. For most people, using a HEPA Cloth bag will be enough filtration. However, for some people, they do need the benefits a sealed HEPA vacuum can provide. I also tell people who use a sealed HEPA vacuum not to worry about the quality of the HEPA Cloth bag and just use the cheapest ones they can find, it's not so important if the vacuum has a HEPA Filter on the exhaust.
Rob