Generally, yes. Some systems may not support or allow non-latin characters. In the backend, the database and other systems need to be setup properly to handle non-latin characters or unexpected things may happen. For example, one multi-bye unicode character may be interpreted as multiple single byte characters (or whatever the expected size is in the encoding being used).
If the system accepts your input, and everywhere where you will be entering the password allows you to switch languages, you should be fine. The one catch that immediately comes to mind is if there is a maximum number of characters allowed and because you are using multi-byte characters you end of exceeding the limit or if it performs some type of truncation. There may also be some type of security filters built in assuming only latin characters are allowed, and your input could be flagged or sanitized. All of these conditions will depend on the specific system and what it supports.
You may need to test and see if there are compatibility problems; however, bonus points for you if it takes your single characters and considers it 2 or more - giving you a longer password without you needing to remember more pieces. If the system accepts your input and it works great. If you ever encounter weird problems, then you hopefully will be able to reset and use a plain latin set.
For reference, just doing a basic text to binary conversion:
passw密码rd = 01110000 01100001 01110011 01110011 01110111 11100101 10101111 10000110 11100111 10100000 10000001 01110010 01100100
(9 "characters", 13 bytes)
password = 01110000 01100001 01110011 01110011 01110111 01101111 01110010 01100100
(8 "characters", 8 bytes)
In a way this is what the computer really sees. So if the system is not unicode aware it may go nuts, or may interpret
passwå¯†ç rd, etc. If the functionality is not implemented consistently throughout the system the function which saves and hashes the password may see it one way and the functions which late compare the hash may do it another way.