Will I receive Explorer card benefits if my employer pays for my flight?

There are two different sets of privileges here, those supplied by the airline program and those by the credit card.

The overwhelming majority of truly frequent flyers (50,000+ miles per year) are traveling for business purposes, where someone else is paying for and oftentimes also booking the flights. So long as your Mileage Plus number is on the passenger record, you will always receive all applicable Mileage Plus benefits for a flight, regardless of who paid for it or how. For example, you can expect to receive all applicable base miles, bonus miles, and PQMs, and for the miles to count toward GPU earnings for 1K members. Once you attain elite status, you will similarly be accorded status privileges such as automatic upgrades, Premier Access boarding, priority standby, etc.

Benefits that are given to cardholders, however, may have some additional requirements imposed by the bank on top of those imposed by the airline, as spelled out in the terms and conditions. For example, provided the Mileage Plus account associated with the Explorer Card is the same one on the reservation, you will still receive boarding group 4 regardless of who paid for the ticket. To receive the free checked bag, however, you must use the card to purchase the ticket:

To receive first checked bag free, the primary cardmember must include their MileagePlus® number in their reservation and use their MileagePlus Explorer Card to purchase their ticket(s).