Ok. The Blades side quests can be done, but you must stop the Main Quest after Alduin's wall.
- It is possible to begin this quest without killing http://elderscrolls.wikia.com/wiki/Paarthurnax by talking to Delphine after the completion of http://elderscrolls.wikia.com/wiki/Alduin%27s_Wall.
So after you get to the temple, give your blood and check stuff out, talk to Delphine about rebuilding the blades. You go get 3 people and induct them into the cult... er group. Then talk to Delphine who points you to Esbern for some 'dragon research' which is a fancy way of saying 'go kill a dragon and get some scales and bones'. So off you go. Your rewards for this are the potion Dragon Infusion, which gives you a permanent 25% less melee damage from dragons, as well as Dragonslayer's Blessing, which grants a 10% increased critical hit chance versus dragons for 5 game days. Look at this one as you would a shrine. Except Esbern is the shrine.
So the Blades are stocked, staffed and handing out dragon locations and blessings. You can keep doing the hunt for dragons in a fetch quest cycle of boredom and snoozery or you can then kick off the next quest in the Main Quest, F the Blades and start meditating on words of power and doing the fetch quests for the Greybeards. Yes, you lose access to the Blades, but outside of Dragonslayer's Blessing, there isn't much reason to go visit them. They don't have anything of note at the temple (which is really an oversite if you ask me- entice my dragonborn ass to hang with them if I'm gonna kill one of the coolest characters in the game.) This isn't to say the Greybeards have all that (because they don't) but I think their fetch quest/"blessings" are better than the Blades fetch quests/"blessing". Plus ... hey ... Paarthurnax is your buddy.
Esbern and Delphine are dikes. Serve the Dragonborn, my nordic ass.