Getting your model just right will become much more complicated initially if the walls of the model are approaching the limit of 1mm. You might inadvertently cause a hole in your mesh for example. Or more commonly, make one part just a tad bit too thin which causes it to not be able to be 3D printed.
If you absolutely positively have to use a 1mm wall thickness, such as in the Chameleon model above, then go ahead. But, we would never recommend that you make large portions of your model 1mm thick. This would lead it to be impossibly fragile and this might make the model so weak that we couldn't even get the support material out without breaking it, let alone ship it to you. Excessive thinness could also lead to errors in the final build.
Look at these pictures of
Christel's Impractical Half Bowl. This beautiful model was ruined by the printer because it was simply too thin. The wall thickness was 1mm, so just as thick as the Chameleon tongue. But, because in this case the 1mm area was not a tiny detail but made up a large proportion of the surface of the bowl and the 3D printer was unable to print it properly.
This is a side front of the model, so far so good.
But if you look at the model from the side you can clearly see, towards the rim of the bowl in the center, where the printer had trouble with printing the bowl.

Here you can see that the models surface is 1mm nearly all the way round.
And a top view shows you the printer error.

You should be able to measure the thickness of your mesh using the 3D software that you use.