Yes. BinBot is the bot account and Bináris is the admin account. The second login throws out the previous one. Respectively:

c:\Pywikibot>python pwb.py -user:Bináris login -all
ERROR: wikipedia:* is not a valid site, please remove it from your user-config
Password for user Bináris on wikipedia:hu (no characters will be shown):
Logging in to wikipedia:hu as Bináris
Logged in on wikipedia:hu as Bináris.

c:\Pywikibot>python pwb.py -user:BinBot login -all
ERROR: wikipedia:* is not a valid site, please remove it from your user-config
Password for user BinBot on wikipedia:hu (no characters will be shown):
Logging in to wikipedia:hu as BinBot
Logged in on wikipedia:hu as BinBot.

c:\Pywikibot>python pwb.py -nolog -user:Bináris userpageprotect.py

pywikibot.exceptions.UserRightsError: User "None" does not have required user right "protect"
CRITICAL: Exiting due to uncaught exception <class 'pywikibot.exceptions.UserRightsError'>