No this is a very bad idea. There is a reason why the baby need to stay inside for 40 weeks. At 36 weeks a baby is considered premature and if you induce labor by any method, your baby could spend long days and nights in a NICU. Term is actually 37 weeks onward, but even still, the baby's lungs may be not fully developed. I think it is more like 38-42 weeks that is term, no closer.
My baby was born at 35 and a half weeks with an emergency c-section from placenta previa, and I will assure you those 14 days visiting the baby with all those tubes and needles and tests going on was heartbreaking and not worth the trade off of the last few weeks of pregnancy.
Besides, pumping at this stage isn't healthy for your breasts. I know it's hard, but you'll make it and having a healthy baby is well worth the end....take it from someone who has been through almost every scenario and has 6 children.