Are you saying there is no induced demand onto side streets from giving more priority to the East Boston on-ramp?
I'm going to guess that is likely the case today, yes.
Keep in mind that the nearest upstream offramp, at Bennington St., is also a special kind of clustercluck - so anyone trying to skip the que has to pay a meaningful time tax before they even get close to the tunnel.
And that's probably also true for 'local' folks today who'd be tempted to avoid the local traffic at the tunnel entrance by getting onto 1A upstream - they too have to burn some extra time trying to get onto 1A @ bennington. (That's true also if they want to take the Ted instead, fwiw).
So on the margin, yeah, i'll guess there's not a direct trade-off between 1A traffic staying on 1A vs. taking a detour through the local streets. Keep in mind that there is theoretically a point at which that would be true, obviously, but the Bennington St. bottleneck is a big enough wedge that scales can tip pretty far back towards the local trip origins before you start seeing a meaningful detour effect.
Which is all another way of saying that I think that any further changes to the advantage of the local traffic is more or less a direct re-balance at the expense of long-distance traffic.
Which is ok, because the no-toll re-design (inadvertantly) tipped things dramatically to the advantage of the long-distance traffic.