Only if your battery pack is a bit feeble or it has small wires.
Your problem is in the pre H bridge stage. It will use a push pull pwm to take the 12v to 160vdc. This is stored in your HV caps. This is all you have to power a surge + the power the little 1000w pwm can contribute at the same time.... so you limited to that supply of energy. The caps on the input will only stabilize the battery voltage giving the pwm a full 13v or whatever your state of charge is.. this may give you a fraction of a boost, but the current limit of the pwm will render any more low impedance oomph unusable...
If your battery is sagging on start up, then short leads, or cap pack may help.... but you need to add more caps to the HV pack inside, this will give the H bridge a bigger reserve to bang into the load, doubling it may get you started... may not. If it had some chance before, it will have a show now... if it had no chance before, it probably needs more than twice... but you also run the risk at some point of over current on the Hbridge fets..... but i suspect they can take a pretty fair o/load for short periods.
Physically getting them into the thing may be a problem, but external mounting is possible with thick wires... never tried. This is where LF inverters shine, as they drive the Hbridge directly from the battery bank, so have basically unlimited surge....... well...limited only by how much the fets can take.... mine is possibly 150X6X50 or 40kw or more for a limited time. The transformers then become the limiting factor ( mine are 90lbs or more now without the kilos of copper windings).
So thats your problem, surge storage inside the unit for the 160v or whatever the USA units run ... ( I assume 110x1.414... ish)
The length of tome of the surge will be determined by the inertia the rotor has to overcome versus the current developed in the rotor bars, working against the stator fields. The start cap will effect how this magnetic dance plays out, as it is the thing that helps drag the a phase around so there is a rotating field. If the start winding is wound with thinner wire, then this will also change the phasal relationship of the windings... so it may not even have a capacitor to keep it simple, but most refrigeration stuff I have worked on do have caps, and a weird replacement for the centrifugal switch that you would normally have in a higher torque start motor.
So try a larger cap in that position as well, it will not run after it has started as it uses a ntc in series with the start fields, so as it gets hot it's resistance goes up very high, and effectively you have disconnected the cap by this mechanism.
If you get an inverter type AC, you will probably have no start issues, as it is a three phase brushless DC motor, and it will have it's own caps there to do the job for you.
.................oztules