Does Sir Gawain live up to the ideal Christian knight as defined in Sir Gawain and the Green Knight?
The ideal Christian knight as defined by Sir Gawain and the Green Knight would have to live up to the code of chivalry. Chivalry would look poorly on those who did not have self-discipline when it came to lust or physical pleasure. It held in high value physical courage, loyalty to one's lord or king, and piety toward God and Christianity. Christianity values love and marriage. It is important as a knight that he be loyal first and foremost to God and his religion and just as importantly to his king.
Sir Gawain from the very beginning shows his loyalty to his king by taking the Green Knight's challenge in the name of King Arthur. Sir Gawain is essentially sacrificing himself by delivering a blow to the man in green knowing in a year and a day, he will also receive a blow with this knight's axe. If Sir Gawain had not taken this pact, the honor of King Arthur and his kingdom would be in question as the Green Knight mocks them.
On his journey, however, Sir Gawain does not live up to the integrity and honesty portion of being a good knight. He makes another pact with a lord whose home he stays at. The Lord, Bertilak promises him his day's returns hunting for whatever Gawain receives during his days at their home. After three days, Gawain receives kisses from Bertilak's wife each day. Each day, Gawain gives Bertilak the kisses. On the third day, in addition to kisses, the wife gives Gawain a sash which Gawain fails to deliver to Bertilak. Throughout his stay, Gawain refuses to be seduced by Bertilak's wife which is honorable and part of being a good Christian Knight.
In the end, Bertilak reveals himself as the Green Knight and delivers one, non-fatal blow, which is meant to punish Gawain for not revealing the sash to Bertilak. However, it is not fatal, because Gawain proved himself to be honorable by not giving into Lady Bertilak.
At the end, Gawain wears the sash on his arm as a symbol of his dishonest behavior and as a reminder to be penitent for this poor behavior. This is a sign of Christian piety - to be sorry for one's sins and to make up for sinful behavior.