My gut reaction is probably not, but that has conditions.
First, debut album. I'm almost glad that I did not discover WDADU until I went to an IAW era concert. If that was my first exposure to the band, I might not have given DT a chance a few later with IAW. So by debut, I'm going to instead change the condition to DT's breakout album.
Now if DT released ADTOE in 2011, probably not. If DT released the breakout album ADTOE in 1992, then probably yes. A lot of my fandom came about not just because of IAW in a vacuum, but because the time frame of the release. It was right around the time I was really going back and forth between prog (early Genesis, Yes and similar), Megadeth style metal and guitar hero shred. DT was the first breakout band to combine all of these elements so perfectly with IAW. Fates Warning and Queensryche were in the ballpark, but Queensryche didn't really have the Metalideth *balls* and Fates Warning weren't as focused and "hooky" in their songwriting as DT.
DT's prog metal brand was going to happen with or without Dream Theater. So if they didn't breakout until 2011 with ADToE, I don't think I would be all that blown away. They might even be relegated to the passing prog metal over-saturated clone dimension where I check them out, but then quickly move on.
The stars really aligned for DT with I&W. Even though metal was more in vogue in the 80s, I'm not sure they would have done as well if I&W came out in 1987-89.