in my opinion the overnight culture of TESE material is possible. We use another procedure; all TESE samples are obtained before the beginning of the ICSI cycle, cryopreserved (if sperm is found) and thawed in the time of fertilization. With this procedure we have very good results and it simplifies the logistic.
I have used this method very succcesfully for years. Our protocol was to either perform the TESE the day before the egg retrieval or to thaw the specimen the day before. The specimen was cultured in elongated micrdrops under oil in a 37 C incubator with 5% CO2. Many times by the next morning, the sperm would start twitching without any pentox being added.
Comments from Eva Schenkman are very valuable. However, it is not always necessary to culture the sperm overnight. Testicular sperm are non motile but gain motility after exposure to a protein supplemented media. Usually 5% HSA supplementation is enough. You may not find them actively moving. The ICSI outcome after injection of twitching sperm is equally good. Cryopreservation of testicular sperm is very successful now and it is highly recommended to preserve sperm even before initiating ovarian stimulation. Performing TESE a day before retrieval and culturing TESE sperm overnight sometimes becomes risky if no sperm are retrieved and the patient has already spent money and efforts for stimulation. Sperm retrieval before ovarian stimulation provides relief. Overnight culture of Frozen TESE is not required and can be thawed in the morning of egg retrieval. You may find this review useful. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3604828/
With the advance of vitrification, freezing oocytes is now a viable option when no sperm is found if the patient is opposed to donor sperm backup. Sometimes, on a rare occasion, with very poor quality TESE sperm, the thawed sample is very difficult to work with and a fresh sample retrieved the day before and allowed to incubate might be preferential. If you have a patient for whatever reason doesn't want to do the TESE off cycle, the day before is a viable option as opposed to the day of retrieval.
It is always better to consider all available options but choose the best. Eva has a good point and in some cases maybe helpful. In other situations, may not be a good idea to leave TESE decision close to retrieval. Oocyte vitrification is available option, however, survival rates vary significantly. On an average loosing 70% eggs after vitrification is more loss as compared to loosing half the TESE sperm. Further, if no sperm found and the patient is not willing to use donor sperm, why to vitrify the oocytes. In my opinion, efforts made to retrieve sperm before oocyte retrieval is preferred and eliminates worries.