I am studying the design of a grid tie inverter and according to the documents I've read through, many synchronize the inverter current output to match the phase-frequency of the grid voltage.
Is this scheme the right one if my aim is to compensate only the active power absorved from the grid (by a local load)?
Yes it is the right one and happens in steady state, but due harmonics and nonlinear loads it is quite difficult to get satisfactory results during transients
Out of the steady state, would I be delivering reactive power to the grid until I accomplish (if possible) to sinchronize inverter current and grid voltage?
The answer to the question you are asking now when the system is out of steady state is not so straightforward. Depends on the network and the circumstances...