The Likutei Yehuda goes on to quote his grandfather, the Imrei Emes zy”a, who says in the name of the Kotzker Rebbe zy”a that chasidim are more connected to Birchas Hamazon than to tefillah. This is because Chazal say (Brachos 31A) that someone who is drunk is forbidden to daven but he may recite Birchas Hamazon (Yerushalmi, quoted by Tosafos ibid).
This teaches us that even someone who is like a drunkard in the sense that he is not on a high level of avodas Hashem can still connect to Him through Birchas Hamazon.