I think you mean dip tube, not dip stick. A dip tube should properly be called a siphon tube or pickup tube, but that's only my opinion which doesn't mean anything. OTOH, a dip stick is typically used to measure the volume in a vessel much the same as a dip stick is used on a car engine to measure the volume of the motor oil in the crank case.
So, assuming you mean pick up tube, the answer to your question would be don't worry about the immersion chiller sitting correctly. It won't matter if it's not perfectly vertical or tilted a little. That's a very trivial issue. Regarding hop pellets possibly plugging it. It has been my experience that pellet hops disintegrate in the boil and basically turn to dust. They will plug up a screen fairly easily. Whole hops will definitely plug up a pick up tube unless you use it with a false bottom or some type of screen. An easy way to avoid pluuging is to put a stainless steel pot scrubber between the end of the tube and the bottom of the kettle. That will strain out anything large enough to cause problems. You can simply wedge it in there. It's easy to install and remove and easy to clean. The best part is that they are really cheap to buy. I use a false bottom in my BK, but that's an expensive way to go. The reason I have the FB installed is because I sometimes us the BK for mashing when I need the larger volume. It does a great job of straining the whole hops and also holds back a lot of hop debris and trub. You can get buy with just using hop bags and then there is no need to use any kind of strainer or screen. Matter of fact, you can get buy without a pickup tube if you don't mind tilting the kettle at the end to empty the last gallon or so of wort.