I guess it all depends on your positioning. If you get there early enough, and can score curbside viewing, then leave the stroller right there, with the child in it. I wouldn't recommend putting the stroller on the curb and then removing the child.
I have seen people get to the curb area early, spread out some blankets, and then put two strollers, end to end, along the curb....saving about 10 spaces. Not too cool.
But, keep in mind.....if you get to the viewing area, and there are folks in front of you, you aren't going to be able to move the stroller up to the curb. I had one pretty bad experience with that. My dd and I got to the spot we wanted about an hour prior to the start of the Electrical Light Parade. A CM told us exactly where to stand since she was going to rope off the area, leaving a walkway right next to us. Okay...I'm good with that. Well, dd is 5'10'', I'm 5'8''. But, we got there early. About 10 mins prior to the start of the parade, along comes a sizable family.....about 4 adults with 5 or so kids, one in a stroller. They got in behind my dd and I. After a few mins of banging me with the stroller, the mom with the stroller flagged down a CM and complained that she couldn't see over the people in front of her...that her child, in the stroller, was completely blocked from seeing the street area. The CM asked my dd and I to try to scrunch into the space of one person...well, that didn't work. And again the woman complained. The CM told my dd and I that we had to sit down on the street. So, there we were, two sizable people, trying to fit into a 3' sq area... and the woman behind us still complaining that those adults should have given her the spots on the curb so her kid could see. And then, the toddler promptly fell asleep. And there I sat, trying to keep my long legs out of the street...same with my dd. And my bad knees are cramping up. It was awful. No more parade viewing for me. I am more than happy to move aside and allow a little one to see better, but for someone to come along, just prior to the start of a parade and then expect those who have been waiting to give up their spots so her toddler in a stroller can see?? No, not dealing with that again. My legs/knees were screaming the rest of the night.