I always thought of it in this fashion: imidazole or DMAP are somewhat nucleophilic and can attack the silicon center much better than TEA. They are also amine bases, so they can act as proton scavangers as well. I personally run such reactions with 2+ equivalents of imidazole instead of using imidazole and TEA. Both are cheap and easy to handle. I also, frankly, always felt that the amine attacks and displaces the chloride, rather than making a 5 bonded silicon anionic species (silylinium as you say?). I have heard of such anionic species being proposed as a SuFEx intermediate, but the idea is really the same for this.
Corey does comment on this as pgk said:
7: This process seems likely to proceed via N-dimethyl-tert-butylsilylimidazole, the conjugate acid of which can be expected to be a very reactive silylating agent.
I do have one point of contention with Corey's paper though. He states:
...the use of imidazole as catalyst and dimethylformamide as solvent proved to be exceedingly effective...
In my hands the use of DMF vs another polar aprotic solvents such as MeCN or THF to make TBDMS ethers was not important. I only used DMF where solubility of the starting material was an issue.