Not really, because Rs also have the choice of "somewhat oppose" which can be interpreted as "mostly support" according to your logic. Hence, it is proper to count the "somewhat" questions as stated i.e. either support or oppose. The fact of the matter is that most Rs tend to avoid 'extreme' answers on Likert scales i.e. 'strongly oppose' or 'strongly support' and tend to select more moderate positions on either side of the scale.
Wojtek