Yes you can use creatures with summoning sickness to pay for convoke costs. Summoning sickness means:
302.6. A creature's activated ability with the tap symbol or the untap symbol in its activation cost can't be activated unless the creature has been under its controller's control continuously since his or her most recent turn began. A creature can't attack unless it has been under its controller's control continuously since his or her most recent turn began. This rule is informally called the "summoning sickness" rule.
Casting a spell using convoke is neither attacking, nor activating an ability with a tap or untap symbol in its cost. Convoke is just another way to pay for the spell in addition to tapping lands like you normally would.
Note that while tapping the soldiers helps pay for the cost of the spell it isn't actually adding any mana to your mana pool, you tap them instead of paying mana.