He was indeed still alive during this chapter, as not only did he lift boxes, but he also cried about the move. However, what isn't clear is if he actually went on the boat, or that was just a hologram, with him staying behind (on page 22 of the chapter, page number 166, we see him suddenly start shaking, and a couple of pages later, he's still in the same position, so it's possible that he died midway, or the connection is starting to cut out due to the distance causing the hologram to get stuck) - however, since we don't have concrete evidence of about whether the robot girl answers to what the professor is saying whenever she talks to him , or just attempts to guess what the professor is trying to say (throughout the story we hardly ever have any speech bubbles for the professor, though I suspect he does, since it seems she is hitting the mark more often than not), so it's also possible that the professor is indeed just nervous about it. Personally I feel like the professor is indeed on the boat.
The likelihood that the professor survives long enough for them to reach the states (and then the survivor settlement) is actually a lot better than her being the only one reaching (and might thus end up getting medical treatment, that while it might not save him, could extend his life). Though even more likely is that the boat sinks midway as it doesn't seem like one meant for such a voyage. Then again, who's to say there aren't other boats they might switch to on the way.