I have now used it without the string tree both at home and with the band and I haven't noticed anything disturbing. No sitar sound, so I'll do fine without it.
My final say on this thread: although I did not have any tonal troubles without the string tree I had to put it back, because I'm a rather hard strummer and the high E string kept jumping off the saddle groove when I was playing with the band. The first time it happened was a funny incident, because there was no snapping sound, the string just disappeared from the fretboard. Heh.
In the end I got me one of these Fender Ultra String Guides. There are no sharp edges in it and it's a bit higher than the original one, so the string angle is not that bad anymore. Thanks for the tip!
Thanks for reporting back. Yeah, that E string might want to jump that nut. If you play hard, you may want to leave a little more meat on the nut in the future. I like mine low like that, but I don't play hard.
The more I learn about them (I have a set as well), I think staggered tuners are an expensive solution in search of a problem that string trees don't already solve.
I would still use a string tree even with staggered tuners.
On my last build I had an issue with the G string ringing a little behind the nut, so Kluson supremes were installed to fix it. Still gonna use the string tree tho