Filler, when correctly placed, should not affect the lower lids. Cheek filler is typically placed very deep to add volume over the cheek bones. This can actually lift the lower lids slightly. When placed higher or too superficially, it can add weight to the eyelids, or cause swelling that affects eyelids position or appearance. See a qualified injector in your area and discuss these concerns before having any injectables.
The answer to this is "not normally". My preference for filler is natural fat transfer. When this is done deep and along the orbital rim (lower boney part of the eye socket) we can actually get more support to the lower eyelid and lifting of the lower eyelid while the lid-cheek junction can be filled and smoothed. Be very careful about any skin removal to treat this because in my experience skin removal is rarely indicated for eye rejuvenation. Small amounts of dilute filler judiciously placed can help with some fine lines beneath the lower eyelid margin.Augmentation of the cheek bones themselves takes quit a large volume to create any change and again, natural fat transfer is the best option. Careful volume enhancement of the cheeks themselves should not create any problems with the lower eyelids. Almost any filler can be used and it doesn't need to be diluted. The results are temporary. Sculptra is another choice and is longer lasting but needs several expensive injections and was first indicated for AIDS facial wasting, but can provide a nice but not specific volume change.Good luck. I also hold a medical license in Utah and many of my family live in St. George. I know there are several fine board certified plastic surgeons who could provide with with choices. I would not let paramedical or even nurses treat the lower eyelids unless they have very unusual experience and training.