I did a test on this last time I installed struts. I had tires about to be replaced, and I left them on afterwards w/o an alignment to see what happened. My conclusion was yes, it needs to be done if you have tires with good life left in them. Full story:
Car was 2002 ES300. I measured the front ride height on both sides as precisely as I could before touching it. I pulled the suspension and changed ONLY the cartridges with OEM units, and re-used the original springs. So this was a milder change than a whole new ready-strut, for example. When I put it back together, the measurements were exactly as before as closely as I could measure (by tape and eye, no way to use micrometer on this!).
Within short order it was apparent the tires were wearing badly on the edges, both sides. No great loss as I was getting new tires anyway. I probably did loose some life out of the tires, but it was worth it for the lesson demonstrated to me.