The pickup note is generally a weak note preceding a strong first note in the first full bar. This seems to maintain the conventional strong one and third beats on 4/4 time. But isn't this an illusion? That is, by beginning the first full bar with the pickup note, the music would be played instead with a strong second and fourth beat, and the first and third would be the weak beat. In other words, it would be obviously syncopated, which is hidden by including the weak note in a separate, incomplete bar. What do you think?
Think about words -as used in a song. Each word of more than one syllable has an accent on one of those syllables. 'SOMEthing' comes to mind. Put this in a song situation, and it sounds best starting a bar with SOME. If the anacrucis was used, the word would come out as 'someTHING. It wouldn't sound as good. 'myOpia' would work as an anacrucis because the first syllable (my) is not as pronounced as 'O', so it (O) naturally falls on the first part of the next bar. Why anyone would use it in a song, I don't know. It's a bit short-sighted.
This explains words in a song situation, now for notes in a tune. One on one is a very common state for tunes. As in the first beat of a bar is played with the first note of a chord (obviously the chord underlying that bar) and often the preceding bar contains a run up to that note. That note would sound anachronistic if it came before the bar, or on ,say, beat two. It just sounds and feels right when the new bar starts and the note is played.( I'm not even thinking of 'push notes' here). So a good player will do the anacrusis slightly quieter (with less emphasis) to state the key note at the beginning of the next bar. That, after all, is the target from the pick up.
Having stated all that, music is there to be manipulated in whatever way the performer wishes, so, as the song goes, anything goes.By moving emphases about, you keep the listener on his toes and interested, so this is a mainstream answer.
Think of the UPBEAT as part of the last measure of the tune. In fact, the UPBEAT beat is 'stolen' from the last measure. If you start the count from the beginning of the last measure you will get a full measure with the strong and weak beats in the right place. This will make the most sense when you repeat the song - all the measures will count up and comply with the time signature.