Can OLS regression be used to predict from a complete sequence of data? Reading online and following this example from scipy I understand OLS can be used to find data between gaps in a sequence (interpolate?) but I already have a complete sequence and want to predict the future of it (extrapolate, i think). Can OLS be used for that?
Ordinary least squares (OLS) is an optimization method to find the best parameter estimates for linear regression, gradient descent is another.

Regardless of the specific optimization method, linear regression is not appropriate for predicting sequence data. Generally, time series methods are used to predict sequence data.