Do table 1 and table 3 have referential integrity on?

Yes

You won't be able to delete records if there is a joined record in the other tables then.

So a cascade delete in a single relationship affects all networked relationship with referential integrity.  Not just the two tables in the immediate relationship?

If referential integrity is on, you won't be able to delete a record from Personnel if there is a related record in any of the tables that have a relationship with it with referential integrity. You'd have to delete the records from Table1,2, and 3, and then delete the record in Personnel. If you try to delete a record in Personnel you should get an error about related records existing in another table. If there is no joined record in table 1 and table 3, the delete will probably work with just table 2.

Cascade deletes are very dangerous IMHO.  I NEVER use them and only delete sparingly and very intentionally.

Before you get too far down the road you might want to check out the Don't Delete Data video.
In conjunction with that how to Archive Records when you need that space back.

In addition, they won't work in a split database when and if your db becomes large enough.