I unpacked my Wraith Stealth cooler, thinking there was a protective film on the thermal paste, and a few bits of dust stuck to the pre applied paste. Will it have any problems cooling my Ryzen 3 1200?
Depends how thick the dust is. Most of the heat transfer from CPU to heatsink isn't via the paste, it's via metal-on-metal contact. This is why you can attach the CPU without any paste and it'll still work (it'll run about 20-30 C hotter, but it'll work). The only role of the paste is to fill in microscopic air gaps. Paste conducts heat about 100x better than air, but metal-on-metal conducts heat about 100x better than paste.
If it's a fine mote of dust, it'll probably have little to no effect. When you clip on the heat sink's compression straps, it'll squash the dust down flat. But if it's a bigger mote of dust or there's a lot of it (or worse, there's dirt or hair), it'll prevent the heatsink from sitting flat on the CPU, reducing metal-on-metal contact.