Yes and No. Note that something is wierd: 600 VA transformer and 120 * 2 watts or 240 Watts.
You could say that something is amis and it is. You need the current of 3.87 A to support the 8 ohm load: Using (I^2)*R or (3.87^2)*8. You also need voltage to support the load. If this were a custom transformer, you could get buy with 38 V * 4 @ 3.87 A; 300 VA, but that probably won't happen. 4 x 38 V would be how a torroidal transformer would be specified. You need the windings to support the current, BUT only one half can be active at anytime, therefore the core VA could be less.
I went the custom torroidal route, but didn't at the time (30 years ago) understand the significance. I went with 4 x 35 @ 3A and I had a supposed 100 W/channel amp. ( I^2)(R) is 9*8 or 72W. Interestingly enough, the guy that designed the amp (Marshal Leach - search for Leach Amp) suggested a 3 A total. In the article, he appeared to be driving electrostatc speakers, thus he didn't need the current. I eventually went with the 4 x 35V @ 3A with 9600 uf x 4 capacitors which gave me separate supplies for each amp. I also have a 500 VA Ac regulator on the input. I did use a 70 V CT (Constant Voltage Transformer) at 16 A for a while and the amp sounded really good, but the hum from the transformer was excessive. The AC regulator made a big improvement. The 4 x 35 V @ 3 A custom cost me $120, 30 years ago. The AC regulator, I picked up on Canal Street when I was visiting NY for $120. It retailed for about $1000. 40,000 uf of capacitance is pretty nasty to handle on power on, so I had to deal with that.
I would reccomend that you size the current for a 6 ohm speaker rather than 8. 8 ohms is the nominal impedeance of the speaker. The more current you can supply, the better the bass will sound.