Doug,
It depends on what you are doing. Also how is your data access being handled, is it remote views or sql pass through? Are the queries filtering out unneeded records effectively or are they grabbing all the records they can and filtering later on the client side?
In some situations sharing connections cna be a performance disaster, in others it is a godsend. As a rule of thumb, if sharing connections causes serious performance problems it is probably advisable to review how you are managing the data access.