No, it's not strictly necessary, though as a general thing you'll still have to convince them to expend their time (and travel if applicable, unless you're willing to compensate for travel). Probably some take personal pleasure from performing the ceremony and will do it if they simply consider it a worthwhile couple, others may do it strictly for personal friends, if at all; conversely, some may only perform ceremonies for long time members of the CoS or whatever other qualifications.
On the precise opposite side of the coin, I'd add that most couples considering this will prefer one or another official as a personal friend or someone they hold in particular esteem. After all, it's just as important, if not moreso, that they be completely satisfied with the proceedings.
"The devil I'll bring you," answered Hagen. "I have enough to carry with my shield and breastplate; my helm is bright, the sword is in my hand, therefore I bring you naught."