Entirely possible. I have done many hundreds of leadless 0.5mm pitch packages (inertial measurement units, sensors etc.) and every time I'm surprised how well it works out. My hands are a bit shaky and I'm never able to position them correctly on the pads. As long as solder paste print quality and paste alignment is OK (so concentrate on your stencil technique!), even gross misalignment of square-ish LGA packages seems to work out, 99% of the time.
Now 0201 is a bit hard to grab with tweezers, and when you place small parts like that you inevitably touch the paste with tweezers, so wipe them clean after each placement. All entirely possible, but if you have to do hundreds, it's going to suck.
Tools: I tape or glue a few spare boards (of exact same thickness, this is important, so preferably same design or something of same stack-up from same manufacturer)) on a melamine board, so that the PCB to be produced snugly slides between and stops at a repeatable spot. Then I just tape the frameless stencil from one edge so I can lift it. Then I use an expired credit card or similar as a squeegee to spread the solder paste. I have made batches of up to 30-40 boards with consistent enough print alignment and quality like this. Can't get cheaper than this.
It's worth quickly checking paste print quality with a microscope or a loupe as you can clean and repaste in a minute, but if you commit to carefully placing 100 components on a poor quality paste print, you lose a lot of time.
I used to have a simple DIY vacuum pick up pen, but really, tweezers are fine. If you do large batches, you should be just using a contract manufacturer anyway. The point is to get a few prototypes done quickly.