I have no experience with airless tires, but I would like to comment on what I have heard, and my opinion of standard pneumatic tires.
Airless tires have a reputation for being extremely sluggish and slow, and while you might think "but I will ride slowly anyway,' maybe you will be working as hard to move along at 10 mph as others will be to move at 15 mph. This is because the 'rolling resistance' of tires is realy the energy needed to compress the tire under your weight as the wheel turns... air takes little energy to compress, but microcellular polymer balls likely take a significant amount of energy.
Also, the nature of airless tires, the micro-cellular ones you linked to included, is that they do not have the shock absorbtion of a standard pneumatic tire, so they will not be as comfortable, and may lead to increased fatigue and discomfort over longer rides. THere3 is a very similar reason for this as above - a standard pneumatic tire will absorb shock like a light spring, while microcellular balls will absorb shock like... well, like a tire full of tiny balls
Lastly, if decent quality tires are used, and they are properly mounted and inflated, standard pneumatic tires simply don't get that many flats! And after a few tries, a flat tire can be fixed in a minute or two. Unfortunately, a lot of regular cyclists have repeated flats for any number of preventable reasons and don't know that this doesn't have to happen.
All that being said, if you can find some airless tires to fit your bike, they will most certainly fill your requirements for flat free riding. Just be aware that there are trade offs that many people do not consider acceptable. By trying the airless tires for your purpose, you are being a guinea pig for the rest of us! If you do get them and use them, please report back on how well they work. Like I said, I have no personal experience with them, but rely on the opinions of others who have tried them.