I would say that there certainly is "a chance," but to find out exactly how much risk there is, I have posted a query in this thread:
viewtopic.php?f=7&t=477&p=191182#p191182
Now, going back to capacitor replacement, you said you might wish to replace all the caps on the Analog Board. I personally have never taken time to do that because none of my analog board caps are leaking fluid all over the Analog board, nor have I experienced any serious problems that I would attribute to the analog board. Nevertheless, you do have a good point about replacing the old caps on those Analog boards. But rather then take all the time and expense to replace everything, you might save some time and money just by using an ESR meter. Although the following YouTube video is talking about the repair of an LCD monitor, the use of an ESR meter in that video is very applicable to capacitor replacement in any vintage Mac computer.