I believe they did, though there are no records they did.
15+ yrs ago I did predator control for several ranchers in Box Elder county, UT. In the mountains to the North and West of the Great Salt lake, there are several sites with definite Spanish markings. They most likely did silver mining out there, though there is gold in a number of areas as well. There are several locations in the Wildcat Hills area that have evidence of very old mining activity, at least 100 yrs or more in my opinion.
I spent almost ten yrs doing predator control and spent many days and nights in the north-west end of the GSL area. A lot of the sites/signs I saw, were on private land and the owners did not allow any public access at any time, the sites on their land are in good shape with no sign of vandalism.
You should be able to find signs in the Lakeside mtns, the Newfoundland mtns, the Grassy mtns, the Silver Island mtns, and the Hogup Range; since there are silver mines and claims out there (some claims go back to the late 1800's, with evidence of mining much earlier). My uncle used to prospect out there, and had several silver claims in the Newfoundland mtn range, I went several times when I was about 9 or 10 yrs old (that was almost forty yrs ago). He had a claim in the flat of one valley (out by the Cedar mtns) that he pulled nice silver/lead ore out of, it was just a hole in the ground that went down about twenty ft or so and then a tunnel for a ways.
Watch out for the bombing range, the air force doesn't like you trespassing at all, they have no sense of humor.
On the North end of the GSL, there are some nice petroglyphs that look like there is Spanish markings mixed in.
My uncle has dementia (he is 73 yrs old) so I can not get much info from him, just what his wife has told me. She does not remember very much about the areas or where the claims were. She got rid of all his notes, maps, and etc.