The heatsinks help get heat off the stepper drivers (on a solidoodle board the 4 black chips lined up under x,y,z,e). This is the only place you really need them, the processor and other IC's don't (or at least shouldn't) get hot.
The stepper drivers have thermal protection built in which shuts them down temporarily while the temperature goes back down - this presents in prints as layers offset (if x/y driver, common) or missing/partial layers (extruder driver). Keeping them cool prevents this from happening (and it's most likely to happen during a big print and waste a bunch of your time and plastic). The little stick-on heatsinks are a great idea (make sure they don't short anything out or prevent you from adjusting the vref trimpots), and if you're looking for a permanent and tidy solution for airflow I'd recommend putting a regular computer case fan (any old one will do) over the board (print yourself a mount for it) and wiring it directly into the 12V power supply wherever's convenient.
Regarding the blower and tube idea: blower and fan are electrically the same, so follow the usual routine to g-code control it (mosfet board if required, firmware, etc. - depends on your setup of course). Two-pin is fine, red=12V black=ground. 3-pin fans have a speed sensor on them that comes back through the yellow wire, even computers usually only use this to confirm it's running for protective reasons! Closed loop control certainly not required...
Blowers usually give better pressure than axial fans, so it's a good choice for what you're planning. I have no idea whether it's been tried before. The tube will be a fair bit of flow resistance, but of course it's worth the experiment. Make the tube as large a diameter as you think you can get away with (but then there's the weight/flexibility thing to tradeoff). Have fun, please share the experience!
SD3. Mk2b + glass, heated enclosure, GT2 belts, direct drive y shaft, linear bearings, bowden-feed E3D v5 w/ 0.9° stepper
Smoothieboard via Octoprint on RPi