It won't work because the LM13700 requires a current source (that sources current into pin 1) and that circuit is a current sink (sinks current to 0V). The LM13700's control input on pin 1 goes straight to the base of a transistor (IIRC) whose emitter is connected to the negative supply rail. You can't feed unlimited current into that pin; if you do, you'll damage that transistor at least.
With that circuit, the collector of the output transistor can't go more than about 0.7V below the 0V rail because of the collector-base diode. So when you connect the transistor's collector to pin 1, heavy current will flow from the 0V rail, into the base, through the collector-base diode, out the collector, into pin 1 of the LM13700, through the base-emitter junction of the input transistor, and out to the negative supply rail.
Two diode junctions in series can't have more than about 1.4V across them without blowing something up. If the negative supply is -15V, that's what's going to happen!
You need to change the exponential current generator so it sources current. Where did that circuit come from?