Not really. HCl, Hydrochloric Acid can only ADD H+ ions, and LOWER the pH.
If you really want to nit pick, however...
At temperatures below 25 degrees C, the pH of pure water is slightly higher than 7.0. At 15 C, it's about 7.16, for example. So if you take cold water, and any such a tiny amount of HCL that it won't lower the pH below 7.0, you can have an HCL solution with a pH above 7.00. (But adding the HCl still lowered the pH a bit).