Let me start by defining HEPA Filter. It stands for High Efficiency Particulate air filter. From what I can tell, the term "true HEPA" is used to refer to where the filter is placed in the unit in conjunction with the motor. This is more of a consideration for HEPA vaccuums (which have exhaust) as opposed to the stationary room filters. When something says it is a true HEPA, it is basically saying that its efficiency in removing certain contaminants from the air is 99.97% effective at removing particles that are .3 microns and larger in size.
To get an idea of what that means, here is a list of contaminants and their sizes:
Pollen 10-60 microns
Mold spores 1-60 microns
Lint 10-60 microns
Dust 1-60 microns
Bacteria .25-20 microns
Smog .05-20 microns
Tobacco Smoke .05-5 microns
Viruses .01-.1 microns
As you can see from the list above, HEPA filters are most effective at removing all of the things in that list except viruses. But you can see that the things it DOES remove are the things of concern to CFers.
Ionic air cleaners work by breaking up the contaminant and pushing it around the room in a different--ionized--form. Ionizing units are great for removing odor, and many people like them because all you have to do is wipe of the metal plates inside the unit as opposed to changing out filters. The technology is coming along to make ionizing air purifiers better, but as a CFer I would urge other CFers to steer clear of them.
You asked if the optional ionizing function is okay. Yes, this is okay. If you need to deal with a strong contaminant that may have a particularly problematic odor, I recommend using the ionizing function while you are not in the same room where it's being used.
Many people are attracted to air purifying units (like the Ionic Breeze or the Living Air Purifier) that do not have filters that need to be replaced. Although the idea of less maintenance and less expense is nice, I strongly recommend biting the bullet and getting a unit with filters that can be replaced. My reasoning on that is based on my understanding of mold spores. If you have a unit that has been sucking up mold spores but you never physically remove them from your home, you are only perpetuating the problem. Mold spores can lie dormant for long periods of time and can flare up again when just the right conditions are in place. If you are sensitive to molds (perhaps if you have ABPA) this can be a problem.
I hope that has been helpful. If anyone else has other questions about how to effectively keep their home as allergen free as possible, please let me know and I'd be happy to help.