Maybe, maybe not. I would hold off on the bebuild until you have the money for the new PSU. If you rebuild and the old PSU decides to go out/blow up it could possibly take new parts with it. Check out this list of power supplies for a better idea of where you LC power rates:
http://www.tomshardware.com/forum/id-1804779/power-supply-unit-tier-list.html
Tier four - Not for overclocking systems or high end gaming rigs. May not even output labeled power and fail standard ATX specifications slightly. May even use cheap components to meet a price
Aerocool
Strike-X series
Templarius Imperator series
Asus Atlas
Cooler Master GX / GX lite series (The GX 450 non-lite Watt model is fine)
E-power units
FSP Raider series
Futurepower
Hiper Type M (Less than 600 Watts)
HIPRO
LC power <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Lepa MX-F1 series (Trigger-happy Overcurrent protection and very poor quality capacitors)
Masscool
MGE XE
Mushkin HP series
NorthQ 4775-500S / BU
NZXT
Hale82N 650w
Hale82 V2 700w
OCZ
GameXStream (less than 1000 Watts, if manufactured before December 2007)
GameXStream 1010 Watts (it's an 850 Watt unit in disguise)
ModXStream (if manufactured before December 2007)
Fatal1ty 2013 550 and 750 Watts
StealthXStream (If manifactured before December 2007)
Scythe Kamariki
Superflower Amazon series
Ultra
Xfinity series
U2 X2 series (Less than 700 Watts)
XVS series
Xion Real Power series
Zalman ZM-700 GLX (Su'scom capacitors all round)
You need a minimum 500watt power supply with at least 28amps on the +12 volt rails with at least two 6-pin PCI-E power leads to run the entire system, per Nvidia. Your PSU only has ONE PCI-Ex power lead, and using an adapter may very well overload a 12volt rail. Something else to consider is that the 8350 processor is a 125Watt processor, plus the rest of your system requirements. I would look into a quality 500watt - 650 watt (anything in that range). In that Tier list, look at units in Tiers 1, 2A and 2B. Currently some of the best PSU's are the EVGA G2 and P2 series, at pretty reasonable prices