How does A* Work with dynamic scene loaders

If I am using A* For a large world which needs to be loaded in piece by piece, would this cause issues with the path finding? If so, is there a way to make it so that it works?

(here is an example of a dynamic loader - https://www.assetstore.unity3d.com/#/content/8015)

There is no built in support for it, but it is not very hard to do.
The pathfinding system has support for saving graphs to files (see http://arongranberg.com/astar/docs/save-load-graphs.php).
The most common solution is to create a grid graph (assuming grid graphs here) for each tile covering the tile and some margin around it (maybe up to 50% or more into the surrounding tiles depending on your game), you could then load these graphs as they are needed. Only having one graph at a time is often best, multiple graphs can be used, but it can sometimes be slightly tricky at the edges between them, therefore I recommend a single graph loaded at a time but with a margin around it so that the player will be able to request paths to places slightly outside the tile the player is currently inside.

Ok thanks! I think I would have to have, at a minimum, two graphs loaded. Though I could overlap the graphs, and not load the 2nd graph until the player is off the old map and far enough inside the 2nd map that the other graph is no longer needed. The only issue I see there is a short shudder in performance.

(Now that I think about it, I can preload the next graph as soon as the player hits the boarder, and just do a .setactive)

Just for reference, I had in mind something like this:

That makes sense. Even if I used a saved grid, I can still use dynamic objects right?

Sure, you load the graph and then apply all dynamic obstacles.
Loading a graph with node data aims to yield the exact same result having only graph settings and scanning the graph.