SQL performance: Is there any performance hit using NVarchar(MAX) instead of NVarChar(200)

Strictly speaking the MAX types will always be a bit slower than the non-MAX types, see Performance comparison of varchar(max) vs. varchar(N). But this difference is never visible in practice, where it just becomes noise in the overall performance driven by IO.

Your main concern should not be performance of MAX vs. non-MAX. You should be concerned with the question it will be possible that this column will have to store more than 8000 bytes? If the answer is yes, even by if is a very very unlikely yes, then the answer is obvious: use a MAX type, the pain to convert this column later to a MAX type is not worth the minor performance benefit of non-MAX types.

Other concerns (possibility to index that column, unavailability of ONLINE index operations for tables with MAX columns) were already addressed by Denis' answer.

BTW, the information about the columns over 4KB having remaining data in an overflow area is wrong. The correct information is in Table and Index Organization:

ROW_OVERFLOW_DATA Allocation Unit

For every partition used by a table (heap or clustered table), index, or indexed view, there is one ROW_OVERFLOW_DATA allocation unit. This allocation unit contains zero (0) pages until a data row with variable length columns (varchar, nvarchar, varbinary, or sql_variant) in the IN_ROW_DATA allocation unit exceeds the 8 KB row size limit. When the size limitation is reached, SQL Server moves the column with the largest width from that row to a page in the ROW_OVERFLOW_DATA allocation unit. A 24-byte pointer to this off-row data is maintained on the original page.

So is not columns over 4KB, is rows that don't fit in the free space on the page, and is not the 'remaining', is the entire column.

an index cannot be created on a column over 900 bytes. Columns that are of the large object (LOB) data types ntext, text, varchar(max), nvarchar(max), varbinary(max), xml, or image cannot be specified as key columns for an index

you can however use included columns

All data types are allowed except text, ntext, and image. The index must be created or rebuilt offline (ONLINE = OFF) if any one of the specified non-key columns are varchar(max), nvarchar(max), or varbinary(max) data types.

Choosing nvarchar(max) also can affect the execution plan optimizations that are adapted automatically by the sql server engine.