Certainly, yes, but I would recommend changing your process.
First-order considerations:If the vinyl is already damaged by dirt that's been pressed into the vinyl, then I know of nothing that can be done. But let's assume that you start with a dirty but undamaged LP. Some LPs come from the pressing plant with damage, and you can't do much about that. But if it's been pressed in a high quality environment (for example, new pressings sold by Acoustic Sounds) it should be good. The best, quietest pressings I have ever heard are made by Music Matters Jazz using a vinyl formula they call SRX.
Even new LPs must be cleaned before the first playing, to remove surface impurities like "mold release compound" that prevents the LP from sticking to the stamper.
First use a wet vacuum wash, such as a VPI Typhoon. This removes large particles. I do this only once when acquiring an LP, whether new or used. There are lots of opinions about the makeup of the liquid used to wet down the LP, but I'm not an expert on that. I use l'Art du Son concentrate mixed with distilled water.
Second, run it through an ultrasonic cleaner. That removes very tiny particles embedded deep in the grooves. I use a KLaudio and do it before each listening. The KLaudio machine is fully hands-off wash and dry, so it isn't a bother. Go make a cup of tea while it runs for 5-7 minutes and both sides will be clean.
The results amaze people regularly around here, who think I'm playing digital.
Second-order considerations:As others have said, your cartridge / needle geometry makes a difference. Generally, the better ones are less affected.
If you buy used vinyl, watch out for crumbling foam inserts. Box sets, especially classical box sets, used to have thin 12 x 12" foam sheets inside as cushions. Over time the foam disintegrates into powder and gets everywhere. It then seems to bond chemically to the vinyl surface and becomes impossible to remove completely. If someone ships you a LP set like that, refuse and return it.
