Its definitely possible,check out my old sps pico thread,I had a 2 gallon slapped full of sps (title is Who Wants To See a SPS Pico in the nano forums).
Main things are:
1.STABILITY,STABILITY,STABILITY !!!!
2. Good random flow.
3. Good spectrum and intensity.
4. Good nutrient export.
5. Keep your hands of of the tank as much as possible.
6.No dead spots so detrius doesn't settle and cause spikes in Nitrates,Phosphates.
7.Make sure Calc,Mag,Alk are sturdy and test test test.
So good starter pieces would be a Digi,Monti,Green Birdsnest. I wouldn't suggest any Acropora,Millepora,Anacropora or anything of that nature. I spent close to $200-$300 on sps before I was able to even keep them alive. Then once I was ablw to get good color,growth and thriving not just surviving,I dove in head first and loved keeping sps. Got my tank looking amazing and my Coralux temp probe rusted and crashed my whole tank before I could catch it,and lost 2 years of growth and close to $700-$800 of sps,I could have cried lol.
I would invest in a Jebao RW4,SW2 seeming they are about the cheapest controllable pumps. I have had mine for over 2 years with no problems whatsoever using a 500 and 200maH power supply,they stock 1A power supply was way too powerful for my nano. I would definitely upgrade your lighting. Idk what your budget is but Maybe:
- 2 RapidLed par38 bulbs $170ish shipped
-Coral compulsion Par38 55w 18k,which is dimmable which are about $130 shipped
-Or id you want a half way decent Chinese Black Box led light with a half way decent selection of leds (warm white or neutral whites for good color rendition)
-You could also build a DIY light,RapidLed offers solderless leds if you can't solder. You coukd build somewhat that you need for about $180-$200 with dimmers/drivers,heatsink,leds,thermal adhesive,power supply.Rapidled,Stevesleds,LedGroupBuy,Reefledlights,BlueAcro,Reefll all have stuff you would need. I would think about:
-2x BlueAcro Half Mega's (18k) from BlueAcro 2 channel ($60 -/+ shipped) [BlueAcro]
-2x Interveronic 700maH drivers with pot's (no power supply needed $80 shipped -/+ you'll have 2 channels of control) [LedGroupBuy]
-1x MakersLed 12" Slim heatsink and hanging kit ($50 -/+ shipped) [LedGroupBuy]
-1x thermal paste (best buy carries this for like $5)
I hope this helps.