Time to event = 0 in survival analysis? In survival analysis, is it appropriate to have a time to event value of zero for a subject(s). For example, the subject experiences the event on the same date as their date of entry. Does this cause any problem in the usual analytical models e.g. Cox etc.?

Depending on the implementation, software for fitting a Cox regression or other continuous-time survival model might not even accept a survival time of 0. The idea with such models is that you start with 100% survival at time = 0 and proceed down toward lower survival fractions in continuous time.
In the situation you describe there was survival for at least a fraction of a day, so you could include the actual fraction of the day if available. If that's not known, you might use a small value like 0.5 days for the event time.
For a Cox model the exact time you choose isn't important, as the fitting of the model just proceeds from event time to event time without considering the actual time values of the events. Fitting a parametric model does use the actual time values, but if there aren't many such cases the choice probably won't matter much; you could try different time values for the "0-day" survival times to evaluate how much.
