Well OP I would say there are multiple answers to your question depending on what is causing the discomfort. In the case of my significant other, she has liver cirossiss and whenever she orally consumes a dose of Oxy., she has an acute episode of nausea - every time. Now, when she snorts Oxy. she never runs into this problem. Now, this is because of the first pass liver metabolism from drugs absorbed through the stomach membranes and routed to the liver. Drugs absorbed through the nose do not get directed to the liver and directly enter the bloodstream - sparing her the nausea which is an effect of the Oxy. metabolizing in her deficient liver, not the opiate effects itself. The opiate/opioid effects themselves do include nausea, but this is a whole other phenomenon.
And on the constipation question. It all depends on the person, some might be fine for 2-3 weeks & others might be running into trouble after only a few days (3-5). I have personally witnessed someone close to me not shit for 3-4 days from opiates. They went on to be uncomfortable to the point where they consumed multiple large laxative doses only to have them do nothing. Ceasing opiate use was the only viable option as the pain of the constipation started to outweigh the withdrawl (they didn't have some silly habit either, it was quite serious). After about 8 hours without opioids and some 16 hours after consuming the laxatives they finally had bowel movements (multiple). After it was all said and done there was some temporary damage and a very painful experience for the books. This was a lady friend by the way, so the embarrassment factor of this story is quite multiplied hehe...