In Chapter 13 of "A Tale of Two Cities," the reader sees Carton taking on a mythical aspect as he professes his willingness to sacrifice himself to save his friends.  In addition, he is a Christ-like figure:  "Greater love hath no man than this, that a man lay down his life for his friends" (John 15:13).  Certainly, Sydney Carton's words reflect this Biblical line.

At the same time, however, the reader of this novel also finds evidence of Dicken's proclivity toward passive, suffering protagonists, men and women whose virtue comes from bearing up under intolerable circumstances.  This passivity accounts for the lifelessness of Darnay and Lucie, a flaw in his novel as it does not provide Dickens the opportunity to create vivid characters.  And, then, when they are given a dramatic scene, the result is often maudlin.  This tone of sentimentality is probably what has caused you to ask "Do you think he is trustworthy?" since there is an incongruity of characterization.

Sydney Carton tells Lucie Manette,

"For you, and for any dear to you, I would do anything".

Sydney tells Lucie that he is completely aware that he will never be good enough for her.  He has lived a degenerate life and sees no salvation for himself, and tells Lucie

"I am like one who died young.  All my life might have been...I shall never be better than I am.  I shall sink lower, and be worse". 

Despite his despair, Sydney wants Lucie to know that she, in her purity and goodness, has inspired him, and that if anything might have made him change his life, it would have been because of her.  Sydney tells Lucie,

"you have been the last dream of my soul...let me carry through the rest of my misdirected life, the remembrance that I opened my heart to you...and that there was something left in me at this time which you could deplore and pity".

Sydney predicts that Lucie will soon love someone else, and will have a family and happy home with him.  In a clear foreshadowing of events which are to come, he says that he would do anything to ensure her happiness, even if it means sacrificing herself so that she can be with the one she loves; Sydney asks her to remember him as

"a man who would give his life to keep a life you love beside you".

Sydney Carton makes his declaration with complete sincerity.  Lucie immediately "observe(s) a change" in his usually "moody and morose" demeanor; "she had never seen him softened".  He presents himself to her with unflinching honesty, offering himself little hope and asking of her only that she listen to his profession and keep it close to her heart.  Sydney asks almost nothing for himself, and the love he expresses for Lucie is pure and unselfish.  It is clear that what he says is true, and comes from the depths of his heart (Book the Second, Chapter 13).