For the most part, they do. People join these groups because they share a political agenda and have the same style of thinking on given political issues. It stands to reason that these groups can and do exert an influence over their membership. Plus, some people like it when others think for them.
I think groups that support a particular party or candidate greatly impact their members votes. When you have a group of like minded people, I think pretty much the entire group acts as one. Whoever the group supports is the candidate that each member of the group will support and vote for.
Yes I feel that when a group supports a particular party or candidate his impacts the votes of the groups members. Many voters don't take the time to read about candidates and then ideas they support. If they are loyal to their group they will vote the same as t heir group because they feel it is in their best interest.
Groups are by definition, a collection of people who have something in common, and like being together. Therefore people will be influenced by the views of others in the group, and they will tend to come together to hold one view. If the group as a whole supports a particular party or candidate, the members are likely to adopt the group view.
Often we you join a political group that is active you often follow what the leadership tells you, so if the leadership is backing a certain candidate and you are part of that group you are most likely going to be voting for that candidate because he/she most likely represents the ideas your looking for in a representative.