Sure you can.....I have a bunch of 2 gal and less PICO tanks all around the house. The only real challenge is temperature stabilization, but that can be overcome with a little ingenuity and fiddling around. I keep everything that can be kept in a PCO that is kept in thelarger tanks that will grow and thrive under lots of PC lights. A hob type filter is a big asset to the tanks surviveability. The Aqua Clear hob filters are the best choice for this due to their flexibility to be modded into a hob refuge and also add additional water capacity. I would look for a AC50 or 70 to modify into a hob fuge. No real need for any real filtration except mechanical if debri becomes a problem, but with snails and shrimp or hermits etc that should not be a real problem. You want at a minimum 2 to 2 1/2 poounds of good liverock per gal so I would probably go with at least a 5# chunk. Keep the sand bed to about 3/4" or no more than 1" in depth. Place live rock rubble in the hob fuge and chaeto or caulerpa for macro algae. I do not know what lights yu have, but if its a screw in type incandesant type you can use a coral life screw in PC light with 50/50 as a direct screw in replacement. It will have more than enough output to grow leathers, shrooms, rics, lots of various polyps, coca worms feather dusters. Clams and stonies are not going to work but there is still a heap of neat corals that can be kept quite fine. Sexy shrimp are especially nice n a pico tank, as are the small blue leged hermits. I routinely keep watchman gobies, blue neon gobies, clown gobies and on occassin tiny clownfish and rainfordi gobys in my picos. When the clowns get too large I put them in a larger tank or trade em back to the lfs for another small clown....usually they do this without charge. All the others do especially well so far in their 2 gal or less environment.
If heat buildup is a propblem you may be able to add a small muffin type cooling fan to your existing hood. If its too cold, you can always add a mat type non controlable heater that does great to keep tank temp within the required range......or maybe even fit a small 25 or 7 watt heater in the hob fuge. I even run home brew skimmers in all my hob fuges..Just treat it like any other sized tank and you will be fine......water changes, test the waters, get to know the parameters, cycle it like any new setup no different rules apply and set back and enjoy.......I have larger tanks but my main interests is the picos as they can be so diverse and you can have various setups in a bumch of small tanks. I have as much money invested in some of my picos inhabitants as my larger tank has. I guess my only real reason for keeping the larger tanks is for a place to put fish if they become too large for my picos. In the spring and summer months we keep picos in the outside gazeebo and on the back outside patio.....your idea is more than doable.
I do not know the dimensions of that hex tank, but you can buy some nice 9 watt and 13 watt clip on lights that work super with pico tanks and with it not having a hood to hold in heat, heat buildup is not as big of a problem, and yu can always jury rig lights into a smaller compact unit and have a decent looking hood in which they are mounted, and still go upwards on what you can keep in regards to light rewquirements. Picos are good for folks that like to tinker to make odds and ends in small scale or just to have due to their potential and least amount of $$$ needed to have a sw setup. For the most part the majority of foks on this forum are not pico fans and there seems to be very few nano sized tank fans, but saltwater is saltwater its just the quanity of water that differs. Heck they even use MH on pico tanks and keep stonies and clams, so its all totally doable. As one poster stated about evaporation. Its no more of a problem than a large tank is. Percentage of sg will not ber any more or less as compared to sameamount of water evaporation on a larger tank would be. I run most of my picos at 1.023 sg, and they all can drop upward of 3/8" in water level and not have an adverse effect on the overall sg of a tank. I normally top off my picos every morning, but they have gone for 2 or 3 days as well without top offs and do fine. Have fun.
PICO's rock! NO harder than keeping a big 210 gal tank, or a 55 gal....