If I have one battery two controllers and two motors would I improve speed with two batteries?

Complicated answer, but I will give it a whirl.
Under heavy load, battery voltage sags (reduces).
With two batteries, you will have less sag (depending on how you connect them to "share the load").
I already know someone will comment about the last statement.

With less sag, you have a higher voltage (under full load) applied to the motor.
This will give you a little more speed, but probably not a huge amount.

There are two versions of my eBike (under two different brand names).
The only real difference between the two versions is the capacity of the batteries on them.
Both bikes use 48v batteries.
The one with the larger capacity is about 4 MPH faster. (35 Mph, versus 31 MPH).
 
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