When you consider link juice and funneling that to target pages internally as part of a silo which you are aiming to rank then yes too many ads can have an impact even though those links are likely and should be nofollow..
Either way you will lose link juice and in the case of nofollow links this simply means a portion of the link juice is lost to a 'black hole' versus the recipient site receiving when dofollow links are provided...
Therefore be aware of the number of links you have on a page regardless if it is internal or external...
That aside there are many other factors to ranking your website/page.... hence if you want to beat your competitors my focus would be on providing great content as that increases engagement and reduces bounce rates as well as seeking to get links from sites which G trusts and considers to have a level of authority....
Hope that helps! best of luck...