If Greece defaults, can it still stay with the euro? Should Greece default, a forced conversion from euros to drachmas will be a further catastrophe to Greek economy as the drachma will quickly collapse. However, if Greece leaves the Eurozone, but keeps the Euro as a national currency (at least for a year), its value will be kept stable because of the implicit trust in the euro.

There already are precedents of countries using the euro without being members of the Eurozone (Montenegro, Kosovo, Monaco, etc.). Is that possible for Greece?
The Greek banks will not be able to get any Euro to give out, if the IMF and the EU cuts of all the loans to Greece.   Therefore if Greeces remains in the Euro, there will be no banking system in Greece.