Depends on what gets time transported. In the 1632 version, Grantville wasn't a large city and enough of the surrounding rural area came with to prevent initial food issues. Many US farmers have some amount of on site storage and many US towns started as farm product pickup sites for the railroads. A lot of those facilities still exist and could source food supplies. Now if you are taking just central Boston or London and dropping that into a medieval rural setting, food issues will happen quickly. The local police SWAT units might be pressured by city leaders to "Do Something" to obtain food supplies. Or if one came with, the local National Guard base might be looted for weapons and vehicles.Well, after people starve the first year, yes.
Modern city populations are supported with modern farming techniques and machinery. And whenever this transition takes place, the local farmers would have planted for their normal expectations, will won't include the city people - you can't instantly add a couple of million new people into an area and expect there to be food available for them until at least the end of the next growing season.
In this scenario, in North America, you also have the issue that the areas currently planted with grain, and that are used for graxing livestock, are
1) Out of transport range of most city folks who don't have fuel infrastructure.
2) Are apt to be from a historical period in which that land was not being used for farming yet at all. Humans can't eat prairie grass.
Lots of ways to do this. The starting scenario really determines how things play out. Plus how effective the newcomer leadership is in maintaining/keeping control of things while the issues are worked through.
In 1632, one of the early issues was medical supplies. Those on insulin or cancer treatments had to accept that their time remaining was suddenly much shorter. Many drugs can be made from local supplies but learning how and setting up the processes to make them may take more time then the ill folks have. Drugs may not be a priority if food and resisting invasion by the locals are pressing issues.
If things go really bad for the newcomers, it could turn into a version of an RPG module where the local adventuring party gets to explore the mostly deserted place of weird wonders.







