Will outdoor antenna help if reception is max?

A Chicago downtown location. Meridian 504, Nordost interconnect, Grado headphone amp and phones.
Yes and substantially.
Assuming we're talking FM here. Your ideal antenna would be very directional and rotatable to aim at the station. In your location the problem isn't signal strength but reflections from all the buildings around you. The distortion caused by these ghost signals is appropriately named multipath distortion.
Concur with Ghostrider45's posting, but mostly because "multipath" reminded me of "multipass" from "The Fifth Element". :D
Exactly the same antenna, just located a few feet higher improves noise and multipath. Then, just being outdoors instead of indoors also improves these. Finally, being directional adds another big improvement, but that requires a rotator, so added effort to tune every station. Or, if you only have one favorite station, then you'll be loving it, even with no rotator. Signal strength is not the major factor that affects sound quality. Multipath level and interference (from noise and other stations) are much more imperative to control.
If reception is MAX than multipath or multipass distortion is MIN. The roof antenna has much higher gain than built-in or indoor so signal control is up multi-story. Higher level signals are MUCH easier to filter with great tuner such as Meridian.