Will 2 300 Watt PSU's work the same as putting 1 600 Watt?

Solution
Would it work? Yes

Is it recommended? No.

You would need to use or make an adapter to allow both power supplies to have the GREEN and one BLACK wire connected. This would make them both start together.

At the end of the day. it is better to get a bigger power supply to run it all in one shot as no one can ensure HOW things will get along.

A single power supply is also more efficiency than 2 in most cases.
Would it work? Yes

Is it recommended? No.

You would need to use or make an adapter to allow both power supplies to have the GREEN and one BLACK wire connected. This would make them both start together.

At the end of the day. it is better to get a bigger power supply to run it all in one shot as no one can ensure HOW things will get along.

A single power supply is also more efficiency than 2 in most cases.
 
Solution
Theoretically I think that should be possible, but there are some complications that make it impractical:
1. mounting for the two psus
2. adapter cable to allow both psus to be activated by the power button
3. you'd have to load-balance between them manually to make sure neither one is overloaded.
There might be other issues that I don't know about.

Also, a reliable 300W psu will run you about $40 (which means $80 for two of them), but you can get a Corsair TX650 for about $50.