Absolutely - just mix the egg and flour in a a bowl then knead the dough out on the table, wrap it and put it in the fridge for 20 minutes, then when it's nice and firm cut a piece off and roll it nice and thin on a table - make sure you use plenty flour on the table so it doesn't stick then trim it with a knife...
If you want to make shapes or long pasta then you need a machine to roll it out, but get an Imperia one, like a roller for clothes - Imperia - accept no substitutes... Should be around £50, and it comes with the tagliatelle attachment and makes way better pasta than the machine version but without the gluten it's really difficult to get it to stick together if you're doing anything that requires shaping rather than making lasagne sheets... 100g flour mix for every egg you use.
Been a pasta chef for 15 years... Trained in Italy. My one claim in life that doesn't involve me going to hell.