Usually yes. Most residential foundation work runs days rather than weeks, and the disruption is noise, dust, and access rather than habitability. Interior pier work means opening the slab; exterior work means the yard.
More detail
Foundation repair sounds like it should require moving out, and for the great majority of residential jobs it does not. What the work involves by type. Exterior piers are installed from the outside: excavation at intervals around the foundation, hydraulic driving or screwing of the piers, then load transfer and backfill. The house stays occupied and the disruption is the yard and the noise. Interior piers require breaking through the slab at each location, which means dust, concrete removal through the house, and losing access to those areas. Carbon fiber straps and wall anchors are the least disruptive of all, largely a matter of surface preparation and adhesive on the interior wall face. Realistic durations. A typical residential pier job runs two to five days on site. Wall reinforcement is often a single day. Crawl space support work runs one to three days. Longer projects are usually longer because of weather or because the scope expanded, not because the method is slow. What to plan for. Noise during working hours, particularly with interior slab work. Dust, which good crews control with sheeting and negative air but not entirely. Access restrictions to whichever rooms are being worked. Yard disruption and equipment ruts with exterior work, and a conversation about restoration before it starts rather than after. The one thing to expect afterward. If the repair included lifting rather than just stabilizing, interior finishes that adapted to the settled position get stressed by the correction, and cosmetic cracking in drywall, tile, and trim in the weeks following is normal. That is why lifting is done in increments. Settle in the contract, before work begins, whether cosmetic repair is included. When staying elsewhere makes sense: a household member with a respiratory condition and interior slab work scheduled, or a job large enough that mechanical systems come offline. Both are worth raising at the walkthrough, and both are the exception in Greater Cincinnati and Northern Kentucky.