US-based answer. No, the specific instrument approach is not part of the flight plan and is not included in the initial IFR clearance.
The flight plan is just that, a plan. It can change in flight, due to weather, immediate traffic, traffic congestion (enroute or at the destination), or pilot's request. If an airport has a Standard Terminal Arrival Route (STAR) it is common to receive a clearance including that STAR, but because many if not most STARs are specific to an arrival direction and/or a landing direction it is not uncommon for the filed/issued STAR to be changed before the flight arrives.
It used to be the case (and I believe is still suggested in the AIM) that a pilot should file a flight plan that terminates at an Initial Approach Fix for a specific approach to the destination airport. This is important for lost-comm procedures; the pilot would hold over the IAF until reaching their estimated arrival time, and then proceed to fly an approach. This technique was probably easier when a single navaid at the field could be the IAF for multiple approaches; today, with ILS and especially RNAV approaches being far more common than VOR or NDB approaches, filing this way is exceedingly uncommon. Instead, a pilot files and is cleared either via a STAR (which might terminate at the IAF for a specific approach, or with radar vectors to an approach) or direct to the destination airport (in which case they must receive vectors to an approach).
In terms of actually flying the plane, yes, the pilots would "deviate" from the filed flight plan when ATC issues other instructions, such as a clearance direct to an RNAV IAF, or vectors to the final approach course of an ILS. When that happens the pilot may elect to fly the plane manually, or may modify the route in the FMS to fly directly to the specified IAF, or may set the autopilot to heading mode so as to fly the specified vector.
There is no reason to assume an ILS approach (or any other type of approach) is impossible, simply because it is not on the originally filed flight plan route.