Is it possible to detect drift with real time predictions?
You may or may not use ground truth to detect drift.
According to google:

What is data drift? Data drift is one of the top reasons model accuracy degrades over time. For machine learning models, data drift is the change in model input data that leads to model performance degradation. Monitoring data drift helps detect these model performance issues.


In predictive analytics and machine learning, the concept drift means that the statistical properties of the target variable, which the model is trying to predict, change over time in unforeseen ways. This causes problems because the predictions become less accurate as time passes.


Covariate shift is the change in the distribution of the covariates specifically, that is, the independent variables.

So I see data drift and covariate shift very similar if not equivalent. According to these definitions:

You need the ground truth to measure concept drift.
You don't need the ground truth to measure data drift.

In order to measure data drift:

You may or may not need all the training data. If you model the predictors (let's say I fit a gaussian variable to my feature $x_i$, and it has mean $\mu_i$ and standard deviation $\sigma_i$) and save the parameters of their distribution it might be enough to summarize the distribution and you don't need the full training data.
I don't think you need to have the same sample size for the serving data at all.
Data drift needs to be done in a batch way, so you can do it with your API as long as you store the results and analyze them after a period of serving time. It doesn't make sense to say that a single observation has drift unless in very extreme cases.