There is some connection between trust in God with no effort and accepting the yoke of learning Torah. Both of these things are accepted parts of the Litvak yeshiva world but no connection between them is ever spelled out exactly.

The way both are connected are in the sense that it is understood that: if one accepts the yoke of learning Torah, then the troubles and difficulties of making a living will be removed from him. But in fact both ideals on the surface to be totally independent.  What exactly is the connection?
I am not really sure about this even though there is  statement from the Gra about the right path of trust in God is specifically without effort on one's own part. It is not as if the Gra accepts the חובות לבבות opinion about trust in God with effort on your own part. See Proverbs 3:25 the commentary of the Gra there.