Are InnoDB files binary compatible between Windows and Linux?
It's all in the documentation here. It should be OK but see my final point.

Two important points to note:


Copying Data Files (Cold Backup Method)


You can move an InnoDB database simply by copying all the relevant files listed under "Cold Backups" in Section 14.15, “InnoDB Backup and Recovery”.
Like MyISAM data files, InnoDB data and log files are binary-compatible on all platforms having the same floating-point number format.

(Should be OK unless you are running Linux on Sparc or ARM! :-) )

and 


Using Lowercase Names for Cross-Platform Moving or Copying


On Windows, InnoDB always stores database and table names internally in lowercase. To move databases in a binary format from Unix to Windows or from Windows to Unix, create all databases and tables using lowercase names. A convenient way to accomplish this is to add the following line to the [mysqld] section of your my.cnf or my.ini file before creating any databases or tables:

[mysqld]
lower_case_table_names=1


Finally, I think tat this is also of interest, particularly for you.

A lot of water has passed under the bridge between 5.0 and 5.6.

If at all possible I strongly recommend that you do a mysqldump and copy over your data that way.


Export and Import (mysqldump)


You can use mysqldump to dump your tables on one machine and then import the dump files on the other machine. Using this method, it does not matter whether the formats differ or if your tables contain floating-point data.

One way to increase the performance of this method is to switch off autocommit mode when importing data, assuming that the tablespace has enough space for the big rollback segment that the import transactions generate. Do the commit only after importing a whole table or a segment of a table.