It is to my understanding that the reasoning for the Titans taking a 'fatal bite' out of its victim is that it is most probably hoping to absorb the spinal fluid of a Titan Shifter in order to turn back into a human. This is supported by the fact that the Titan serum is injected into the back of the Eldian's neck (where the spine is).
Furthermore, there is no way of surviving due to this fatal bite, meaning that the Titan, under normal circumstances, would never swallow you whole; provided it is a typical mindless Titan. Intelligent Titans, such as the Quadrupedal Titan and the Dancing Titan (Ymir), have held a human whole in their mouth, but they did not swallow their captives regardless of their bodies not at risk of harm inside the stomach-like pocket in the Titan body. This could be due to the uncertainty and lack of knowledge currently disposable about the Titans and risks not wanting to be taken.
Overall, this suggests that a human cannot be swallowed whole. The best possible outcome is losing a limb or part of your hand/leg/arm like Eren did when encountering the 'Santa Titan', but in normal circumstances their arm wouldn't grow back and they'd likely die of blood loss.
Furthermore, this suggests that the Titans are unaware of the section of the body that they're severing, and probably just subconsciously hope that they sever the spine of an area relevant to the transferal of the spinal fluid into the second party.
With regards to surviving inside a Titan provided you've been swallowed whole, the survey corps are the primary people that Titans consume, and few of them are consumed by an individual Titan due to their skills in the field. So in the unlikely event of someone getting swallowed whole, they would be inside of the Titan for a long period of time before being vomited out when the Titan fills itself up. This could be months between expeditions or even years. Nobody would be able to survive that long inside the Titan unless they eat other humans raw inside the Titan or even attempt to eat the walls of the pocket they are being held in.
WHEN EREN WAS HELD INSIDE A MINDLESS TITAN prior to discovering his abilities, it was evident that there were other alive people inside the Titan, but it was so hot in the pocket that they overheated and died while calling for help from the heat. Titans are already known to be extremely hot especially without skin, and I doubt that there is any skin on the interior of the Titan. This suggests that regardless of your physical state when swallowed, it will be too hot to last for a prolonged amount of time inside a Titan without simply boiling to death.