If EPA is conducting an approval review of a pesticide a company wants to market in the U.S., would EPA put scientists paid by the company behind it on the approval panel?

No, but EPA routinely had people who are receiving grants from EPA to conduct studies - including epidemiology claims - on panels that then recommend political action.  But then they stopped, which sent environmental groups who had exploited the system into a rage.

It was never an objective policy, and a few years ago EPA put an end to that, capricious "secret sauce" weighting of some studies over others, and sue-and-settle agreements to create law without Congress by manipulating the now-famous Chevron deference Supreme Court ruling of 1984.

That 1984 case was brought by the environmental lawyer group Natural Resources Defense Council (NRDC) and it made them rich - they now have 700 attorneys, analysts and fund-raisers. They even have one scientist. The Supreme Court in 1984 ruled that a government agency created to have expertise in an area could legislate without Congress by creating regulations. No one thinks Congress should vote on science but friendly agreements with politically allied groups, like when EPA settled with a canoe organization by declaring water a pollutant and sticking a county government with the bill so they could have calmer rafting, are travesties. Chevron deference has been abused as often as it's been helpful. 

NRDC even wrote the EPA ruling on coal power plants for the Obama administration. No wonder they are suing now. EPA is no longer an arm of their organization.

NRDC very much wants allied scholars - epidemiologists rather than biologists, toxicologists or chemists - on EPA panels to plead for their causes. They create statistical correlation, they write exploratory papers that scientists may or may not regard as being worth follow-up. It gets media attention from journalists who don't realize mice are not little people and statistical correlation is not causation.

Neither of those two are what the public sees as science. But EPA did, in the past.

The Obama administration was overtly NRDC-friendly so NRDC and others got allied scholars on EPA panels, until EPA said it was inherent bias to do something for government scientists they wouldn't do for anyone else. So they got rid of people being paid by EPA just like Monsanto couldn't be on panels to approve pesticides.

That forced NRDC to legally argue that giving someone money for their expertise should be credentials to be put on EPA panels, even panels related to policy decisions on the products they study. Their argument is recursive; if they are not experts who should be on the panel, EPA would not have given them a grant, etc. They argued that if chemical and fossil fuel consultants can serve on advisory boards then they should be allowed to have their allies on them as well.

That's bad policy but science media who hate Trump more than they love science have been supportive of this. Look for the New York Times to cheer, and by employment that partisan publication is 10 percent of all the journalists in America.

These suits always get filed in friendly courts, like New York or California, where pleading the alternative - 'why it is wrong for a company scientist to be on an EPA panel but right for an NRDC consultant to be on an EPA panel' - is accepted. And the U.S. District Court Southern District of New York, which covers the rich Democratic bastions of Manhattan, Westchester, etc. was never going to side with the Trump administration, so NRDC will be declaring this a victory over evil Republicans, until it gets bumped up in appeal and then they will lament this new travesty of justice ... which only another donation to them will halt.