Since Aioli is essentially mayonnaise, no. As janixes documented above, freezing turns mayo (and also aioli) into an oily mess.
I have found ove the years, however, that both (homemade) mayo and aioli keep for a reasonable length of time in the colder part of the refrigerator when stored in a tightly closed GLASS container.
If its mayo, vegetable oil plus egg yolks than no. If its aioli, extra virgin olive oil, plus garlic, then no. The fats just won't hold up to the deep freeze condition. They will break and separate when defrosted.
Some forums say you can, however, I found this info regarding aioli if made like real mayo.
An aioli, like "Real mayonnaise has an oil content of at least 65 percent or higher. The ingredients do not fare well as a bonding agent during freezing. According to Michigan State University, the ingredients in the mayonnaise separate during the freezing process. The end result does not have the same texture and consistency as it did prior to freezing...instead, it becomes an oily mess upon thawing.
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I have found ove the years, however, that both (homemade) mayo and aioli keep for a reasonable length of time in the colder part of the refrigerator when stored in a tightly closed GLASS container.
An aioli, like "Real mayonnaise has an oil content of at least 65 percent or higher. The ingredients do not fare well as a bonding agent during freezing. According to Michigan State University, the ingredients in the mayonnaise separate during the freezing process. The end result does not have the same texture and consistency as it did prior to freezing...instead, it becomes an oily mess upon thawing.
http://www.livestrong.com/article/502678-can-you-freeze-foods-that-contain-mayonnaise/#ixzz1lfnVe8tG