Yes, Guan Yu was fully loyal to Liu Bei. There was an instance
when Guan Yu served Cao Cao, and Cao Cao saw the value of Guan Yu
as a warrior, therefore he tried his absolute best to keep Guan Yu
as a general, offering him wealth, housing, women, and whatever
else he desired. Guan Yu, however, continued to tell Cao Cao that
if Liu Bei was found, he would immediately return to his side. He
only served him because Liu Bei was missing and hadn't been seen,
and was possibly even dead. However, Liu Bei was found afterwards,
and despite all the wealth Cao Cao gave him, and all the offerings
that he gave to Guan Yu, and even giving him the famous red hare,
upon hearing Liu Bei's location, he immediately left with red hare
in order to continue to serve Liu Bei, he did not have nearly the
wealth or riches that Cao Cao had.
Short answer: Yes, he was completely loyal to Liu Bei, and only
Liu Bei.
