Does it make a difference if a bearing, its shaft and its housing are all aligned during installation? Definitely.
Here's how bearing manufacturers recommend aligning all the components. When installing a bearing that uses two, bolt-together flanges to hold it in place, slide the inner flange over the shaft, then slide the bearing onto the shaft and nestle it into that inner flange. When you bolt the outer flange to the inner flange--with the bearing sandwiched between them--finger-tighten the bolts. Then, if possible, spin the shaft on which the bearing is mounted while lightly tapping the bearing flanges with a hammer, or spin the shaft while lifting/shaking/wiggling the shaft. The goal is to encourage the bearing to align itself within the flanges so that everything is parallel and centered on the shaft and between the flanges.
When installing a pillow-block bearing--where the bearing is in a cast iron housing--slide the bearing and housing over the shaft, install the mounting bolts for the housing finger-tight, then tap the housing, spin the shaft, or do something to get the shaft, the bearing and the housing into parallel alignment.
The moment of truth comes when the bearing's lock collar is installed. If everything is in parallel alignment, everything will spin smoothly after the lock collar is tapped into place. If the shaft turns hard during part of its rotation after the lock collar is installed (or if there is a subtle vibration when the machine in ran) there is a misalignment that will shorten the life of the new bearing. Take things apart and correct the misalignment to ensure that you don't repeat the repair in the near future.
And here's a you-already-knew-this reminder when installing bearings: if it's a greasable bearing, there's probably a small hole in the outer race of the new bearing to allow grease to get into the balls or rollers. Keep track of that hole so that when you install the bearing flanges, or install the bearing in a pillow block, that hole is below the grease zerk in the flange or block so when you pump grease into the zerk it goes directly inside the bearing. But you already knew that, and I'm sure you never get in a hurry during installation and forget to align the grease hole with the grease zerk....