I don't hear the difference between 昨日 and 機能 as pitch, even though it may well be. It's actually more like stress, in the sense that when listening or speaking I am not conscious of how stress manifests itself, just that it's there. Pitch varies with stress as well, but I can't say I'm deliberately raising or lowering my tone when I speak English. So, probably the same as you're finding.
The course did help with my pronunciation. In fact a number of people commented on it whilst I was doing the course. I think I've lost it a bit since then. I really need to practise more, though. I think that's the key.
The course did teach pitch, but not to use the dictionary as a guide for speaking words in a sentence. The tutor said it was a waste of time memorising these. One example he gave was 雪, which is LH when said in isolation, such as あっ、雪 when looking out of the window and seeing snow, becomes a slow falling pitch in 雪が降っています. ユ is mid high, キ is mid, ガ is low.
Even if you don't agree with this, the fact is that pitches of individual words change in a sentence compared to when spoken individually. It even explains this in Japanese wikipedia.http://tinyurl.com/6wqbmve
On there it talks about the downstep in phrases. On the course I did the emphasis was more on how the pitch fell, rather on whether it fell or not. It's not black and white.
Therefore, learning the pitch of individual words is of limited use when aiming for natural sentence intonation. The sharpest changes in intonation occur to indicate word breaks, rather than to distinguish between minimal pairs.