I'd dare say a small amount of oil can work if there is ample,controlled resupply of heat - why would it make much difference if it is coming from the vessel wall or more oil.
However, I found that deep friers are just not designed for that, relying on the oil fill as thermal mass a lot... even or especially the small "fondue" style ones*.
TL;DR for the rest of post: Advice on deep frying without using a fryer. Use at your own risk.
You are better off with a chip pan/wok/pot and a thermometer for the kind of job where you just want to oil-blanch an ingredient and/or want to minimise oil usage because you do not want to reuse it (eg you want to fry tofu in fresh oil because it tends to be a magnet for the worst flavors it can get from old oil, you want to deep fry something with a strongly spiced and/or unruly rub/breading/batter on it, you want to fry ingredients like carrots or red bell pepper that will discolor the oil, you want to heat the oil very high initially to account for a temperature drop).
The largest plate on even a normal electric hob is around 2000W - same as a medium sized home deep fryer, and pots and pans are optimized to transfer these 2000W to what is in them.
If you are not confident with open deep frying, have someone who is work with you for a while - yes it is hazardous, but manageably so - never leave the setup unattended. especially if no food in oil, monitor thermometer closely. always have something made of metal (nothing else) in reach that can cover the pot. always assume something can boil over. keep clutter away from your work area. use really high-heat oil - peanut, refined safflower, soy, rice bran; not some unspecified compound oil with a 180°C warning. be especially careful with induction, can heat a pot with small amounts of liquid in them alarmingly quick. keep the lid off as long as you are heating. if working on gas, ask someone who has experience in doing so for additional advice (overboiling into the burner is an obvious danger!), i'm electric...
*the small ones that are partially plastic in construction - never managed to set a grease fire, but I think I would be far more at a loss to control one with these things than in a pot...