No you cant! You can see them in one day but not spend the night. For those of you short on time do not try to see too many islands - you will spend more time traveling than on the islands. Ideally, and even for an island close to Athens (and this is pushing it), visitors need one day to arrive and get settled, one day to soak up some atmosphere and one day to depart assuming there is a boat available to where you want to go next. This is the bare civilized minimum and not enough to really relax and smell the bougainvillea. The only possible exception to this is to day trip the Saronic Gulf islands of Aegina, Poros and Hydra and how relaxing that will actually be is a matter of conjecture. If you take the cruise its a piece of cake. If you use regular ferries you cant necessarily meet time obligations with certainty.
Itineraries: To get between island groups a trip back to Athens is often necessary. If you are on a tight schedule and don't have the time to wait for the next scheduled boat (if you' re lucky enough to find one that meets your requirements) often you'll have to go back to Athens or the nearest major hub and start again.
For most people this is inconvenient. Say you want to go from Cycladic Mykonos to NE Aegean Samos or from Cycladic Folegandros to Sporadic Allonisos or from Saronic Hydra to Crete or from Crete to Ionian Zakynthos? Sorry, no direct connections are available so its back to Athens or Crete's Heraklion airport for you.
Flights: Booking a flight well in advance can alleviate this problem. One could fly from Mykonos to Rhodes in the Dodecanese for example, once a week in summer. Not at all in winter. But why fight city hall? Go with the flow, the magical Greek islands are the undiscovered ones, the ones you fall in love with in spite of yourself are the hardest to forget!
Ferries: Ferries have ticket classes, with deck or third class the least expensive. On a slow ferry you will likely stop at other islands on that particular ferry companies route on the way to your particular island destination so you'll get at least a glimpse of other destinations. These ferry routes vary by time of year or tourist season. More in summer, far fewer in winter. August being peak season. The same holds true for fast ferries which are usually about double the price of a normal ferry except some offer express routes which cost more still. On an express, just like a train, the ship wont pull into 5 islands on the way to Mykonos, maybe just one. A fast ferry could cut your ferry time to Crete from 20 hours to 9 hrs but booking an additional sleeping cabin to get some sleep would add to your cost. Many prefer to go 3d class and sit it out or use sleeping bags which is permitted.