no, but here's the drawback - if you are diving without a computer, then you are diving with tables. tables assume a square profile, which means that if you really drop down to 80 feet to see a wreck then spiral up a coral wall slowly for the rest of the dive - so you spent less then 5 minutes at 80 - by tables, the whole dive counts as 80ft. i know you know that from class, but might not be sure what it means. it means that if your first dive is 30 minutes, then your second dive to the same place an hour and 15 minutes later will be 7 minutes...*and that's the maximum*.
you can't dive using someone else's computer because they aren't diving your dive. you are. and your dive is by tables, every time that day or that trip. when the tables say you are done, then you're done, even if others are going for their fourth or more dive of the day. is it a penalty? sort of. but that's the choice you make. the whole point is keeping track of your nitrogen load, and you are using tables.
if this is acceptable, if you have the discipline to perhaps cut the first dive short to save some time for other dives, or if you're only doing one dive a day, then wonderful. problem solved. but me, unless i'm doing one really big dive a day, i'll be using a computer.
if you plan on tables, double check with the op. around here, they want you to have a computer *or* a bottom timer, but are fine either way.
if you are totally aware of all this, please don't take offense. consider it a note to others with the same question who don't have your experience.