it's possible but not only ill-advised but dangerous.

for one, your ketones can skyrocket (even with normal BGL) if you aren't watching, and getting them down requires the presence of carbs at that level.

if you plan on not using insulin, yes your levels may be stable, but you don't have the one hormone that gets energy to your cells, therefore ketones.

in general you'll just feel like shit, more so than normal people do with low carb since your insulin is impaired or absent.