It will affect it...for the worse.
If you have more than one person in a reservation, then two things will happen when the computer runs the EUA logic.
1. The lowest elite level in the group will determine when any EUA may be performed.
2. The EUA will only process if the entire group can be accommodated.
For example let's say Mr. Jones (a Platinum) and Mrs. Jones (a Gold) are traveling on the same PNR and awaiting their upgrade. At the five day window Mr. Jones is eligible for an EUA (as he's a Plat), but because there's a Gold attached to the reservation he will be skipped over.
When the Gold window comes at three days, if there is only one upgradeable seat left, the computer will not upgrade either Mr. or Mrs. Jones as both of them cannot be accommodated in F. However, if two (or more) seats existed, both Mr & Mrs Jones will receive the EUA as both of them can be accommodated.
If we twist the previous example to say the Jones' non-elite children are traveling on the same PNR/reservation then neither Mr. or Mrs. Jones will be eligible for an EUA as non-elites (the children in this case) are not eligible for EUAs and the lowest elite level (or lack thereof) in the reservation determines when the party will be eligible for an upgrade.
Of course Mr. and Mrs. Jones and their two kids can standby at the airport for an upgrade...but by that time it may be slim pickings for F seats.
CO will "split" PNR's/reservations at no charge should you wish to improve your EUA chances. To do this, call your elite line (the number is on the back of your elite card and changes each year) and ask to be "split" off from your group. Your flights will not change in doing so, but for EUA purposes the computer will now
see you as a single elite thus maximizing your upgrade chances. In some cases the ability to split PNRs is also available from the My Reservations section of the co.com website.