Whether or not a demigod should focus on their minions is somewhat dependant on the map. A map like 'brothers' where each general nets xp from two lanes (usually double than normal) makes for a good choice to specialize in minions as it is unlikely each character will gain gold in time to purchase more than a single 2k item making them quite formidable even against demigods. Maps like cataract, with towers very close together are often bad for minions as they will repeatedly charge into them, forcing you to recreate these troops.
Looking at some of the demigod generals:
OAK
Oak's spirits are extremely fast, fly(no pathing issues), cost very little mana to summon and only take one skill set to max (4 points). He also recieves cumulative personal benefits from 'soul power' and I have yet to play a game without maxxing his spirits. Using natures reckoning (item) along with at least one point in divine justice will go a long way in keeping those minions alive. The hauberk of life is another cheap item that will aid in making them troublesome for other players. Oak is one of the few generals I pick up morale with as he can have up to 10 spirits active and up to 6 other minions: 16x4 = 64 damage per point in this skill. Don't expect to play oak as a back line character though, as he needs to be up in the front to put many of his skills to use and his minions require that units die to be summoned.
EREBUS
Erebus much like oak has some very fast minions and may have 10 of them at the time. They cost no mana to summon and also require units to die to summon. Unfortunately erebus's minions do not provide him with any special benefits for having around and are somewhat weak without specializing in them (7 total points). Further adding insult to injury, unless you specialize in mist and a heavy mana build, his minions will die about as fast as you can summon them, as he has no means of healing them. Providing erebus with the forest band would help in keeping his minions alive, but I have not had a great deal of success with using minions on this character.
SEDNA
Sedna is a wonderful support character as she has both a passive area heal, and a powerful single target heal, and I always purchase at least Healers and Archers with her. Whether or not her Yeti are worth summoning is up for debate, as they cost enough mana that you could have used pounce roughly twice instead. They are also very innefective in killing enemy demigods since they are melee and slower than everyone but rook. The most troublesome part about them (all melee minions really) is that they are the first to be targeted by towers, costing you a great deal of mana in the process. Despite both this, and that sedna has no ranged attack, I've still had some success using a complete support build with this character.
QUEEN OF THORNS
The best choice in my opinion for a purely support character. Note that her minions are very skill intensive. It will take a total of 10 skill points (Shamblers, Entourage, Compost) just to get all her shamblers up to full strength, but since both they, and the Queen of thorns have ranged attacks you will often never need to engage a demigod to a fight to the death. Her sheild is also a wonderful skill to keep yourself and other team members alive. Mulch right now is up for debate on usefullness. Mathematically this is probably the most powerful skill in the game, but in practice it is next to impossible to properly utilize since you have to find one of your shamblers and target it specifically, and make sure it is near the enemy at the same time. A reworking of this skill to make it more user friendly is in order, but feel free to put some points into it if you think you can micromanage your troops well enough to use it.
And uhh.. it's not 'cheating' to play generals like assassins
I just wish some of them didn't do a better job of it >.>