I live in South Bend, and this would definately be much slower than the existing line, right now the South Shore Line's weekday once-a-day express trains between Mellenium Station takes 1 hour and 55 minutes, making just 2 intermediate stops in Indiana (plus two more in Chicago). About 9 of these minutes is along the long slow ride in and out of
the Airport terminus, so a train could probably make it from the
Amtrak Bendix Station in maybe an hour 45 to Mellenium, the St. Charles Airline is also a long back-up move. As an example the City of New Orleans is blocked at 49 minutes from Union Station to Homewood, IL via the St. Charles Airline, while it takes the fastest Metra Electric Express train (making 3 intermediate stops) 36 minutes from Mellenium Station to Homewood.
Even after the double-tracking project is completed from Michigan City westward, the line between Michigan City and South Bend only has a couple of passing sidings, that are only used a few times per day for trains to pass. The South Shore used to run nearly every weekend train (every 2 hours, 8 to 9 trains per day) to and from South Bend in 2009 but service here was reduced to todays 5 round-trips per day because of delays at few passing sidings east of Michigan City, cascading and creating delays along the entire route.
Pre-pademic I would rountinely end trips by taking Amtrak home from Chicago (its generally much cheaper to fly into O'Hare or Midway) getting home in 89 minutes of comfort on the Lake Shore (9:30pm CT to 11:59pm ET) or Capitol Limiteds, instead of the extra hour it takes on an off-peak local South Shore Line train (the comparable Sunday night trip is 9:15pm CT to 12:46am ET).
I think that re-running Amtrak onto the South Shore Line is way too complicated and something that could really mess-up the South Shore Line's generally quite reliable operations, if the line between Chicago and South Bend was entirely double-tracked I would think differently.