In theory, you could. But in reality, you can't.

Even with a 2.88gb dag-file the problem is that the GTX1060 uses some amount memory for who knows what, even disabling all graphical output, so therefore the miner eventually still gives an out of memory error.

With PhoenixMiner, this problem started with epoch 238. The "-eres 0" option partially helped until epoch 240.
Gminer handled the problem much better, but now as of epoch 241, it started with that out of memory error.
T-Rex complains for memory, and Lol Miner, hangs when generating the 2.8Gb Dagfile.

Any other way to mine ETC with a 3GB card at least for a few more weeks on jan/feb 2022? Unfortunately, no way.