I have some tubeless ready wheels and tires, but they were delivered mounted with tubes the old fashion way. I’ve been riding like that for more than 800km, and I wonder if there is a problem removing the tube and add some sealant after so long. Especially since I had a puncture from a small nail, meaning the rubber from the tire already suffered a small punch.
Riding with tubes doesn't necessarily affect the tires ability to hold air without one. In fact, I find it easier to inflate tubeless set-ups where the tire has already seen some use, as the carcass gets a bit more flexible.
That being said, any and all holes in the tire need to be sealed. You may have caused some small ones all around the surface of the tire, but those should easily be handled by the sealant. Depending on the exact size if the nail-induced hole you mention, sealant just might take care of that too. If not, it can still be repaired with a dab of superglue, preferably applied to the inside of the tire.
If you happen to have suitable glue easily available, I totally recommend using it before adding sealant, as it has a tendency to make things messier and glue less likely to stick well.
There shouldn't be any reason the mileage would stop you from mounting the tires tubeless. Tubeless tires can be unmounted and remounted with fresh sealant.
The puncture from the nail is another matter. If the hole is large enough that the sealant cannot seal it initially (or can't seal it at all), you may have trouble getting the tire inflated to the required pressure to properly seat the bead. You'll need to patch the hole if this is the case.
Carefully inspect the bread if the tyre.
A tube less the is held in place because the tensile material in the bead is kept taut by the rim. In other words, the bead cannot be lifted radially off the rim as its circumference is only marginally larger than the circumference of its seat on the rim.
Damage to the bead, eg caused by tyre levers, may compromise the tyres seat. This might be immediate damage like abrasions or cuts. Or less obvious damage like over straining the bead by to much stress.
In particular for road tyres at comparably high pressures and typical use scenarios this may be a cause of concern. For example, a tyre blowout at during a fast descent (eg 15m/s) may be somewhat inconvenient.
As an aside: There is a controversy if high pressure by itself is a concern. Jan Heine (Compass tyres) recommends not to use tubeless tyres above 414 kPa (60 psi, 4 bar) at all (cf Heine's blog). Allegedly Conti does not offer road tubeless for similar reasons (no reliable sources). On the other hand are countless posts of cyclists running tubeless at high pressures. And of course several tyre manufacturers offer high pressure tubeless tyres (eg Schwalbe, Hutchinson) – a statement by itself. Schwalbe published also compatibility charts.