Hi ! If you concatenate two datasets, you will need to build a new FAISS index for the new dataset.
Depending on the number of documents you have and the type of index you use, you can either:

rebuild a new index from scratch (easy, but slow for big datasets and advanced index types)
or update one of the existing index with new vectors (useful if you need to add a few new documents for example into an already existing big dataset)
or merge the two index together (possible only for certain index types, here 1 is an example for IVF)

Regarding your second question, it is definitely a reasonable way to search a large corpus. Though it may also depend on your needs in terms of speed and accuracy, and on the size of your dataset.