From what I've read the Kerensky Offensive is completely independent from the US entry in the war, Russia had to attack Germany and relieve pressure from the other fronts since at this point they were entirely dependent on Entente help to survive their war effort and they also hoped to legitimize the Provisional Government, but don't quote me on the second point.
They had to attack and they hoped to be able to repeat the success they had in 1916.
Also the Provisional Government received a lot of its loans (not counting the fact that they were taking loans from the US before its entry in the war) from other sources than the US, for example the Rothschild lent 1 million rubles since they stopped their terrible treatment of Jews.