But the price you must pay to the Star League is fealty to the Camerons. In one form or another it is accepting rulership from Terra and a foreign sovereign. Are the Taurians willing to cast their lot with them or a mutual defense pact committed to the defense of its own members? 
To be honest the TC's likely to tell both sides to *Bleep*.
But embedded in my previous post was the idea that Cameron and the Star League don't need the Taurian's to join, they just need the TC to engage in a serious build up of arms. A build up aided by technology transfer and dirt cheap licenses.
What happens in the 2560's if the Taurian's are starting to produce design's in the same weight class as the Dreadnought or Atreus, or more likely cruisers that would give TH contemporary's such as the Avatar an equal fight.
You get a dynamic where suddenly the FedSun's has been pincered between the biggest Fleet, and a significant naval power rapidly updating and upgrading it's major combatants. Not to mention it's regiments are seeing TH and FWL Mech designs being added to their ranks.
The main goal here is force the FedSun's and the Combine into a major naval arm's building race. A race neither economy is well suited to win at this point in time.
Victory by force, or victory by outspending the other side.
In this setup the FedSun's and Combine are going to need resources now, and the immediate target is the Outworlds Alliance who are going to get steamrolled.
To try and sum up the Hegemony doesn't exactly need the TC to join the Star League, they just need the TC to start acting a manner that shapes the coming confrontation into one that favors it.
Aka turn the fight into one of Naval & Economic dominance, not one of how many / effective regiments one raise.
Sorry hope this helps make my point clear.
Ciao
