'Effect' can be a noun (meaning, primarily and inter alia, the result of something) or a verb (to cause something to happen i.e. to bring about).
Although I am unaware whether or not this is necessarily the issue in question, 'effect' is prone to confusion with 'affect' (in brief, a verb meaning to have an influence/impact on something/someone).
Here are some examples:
'Is Sally's depression an effect of her father's death'. - 'Effect' = noun --> is the depression is a result of her father's death?
'Sally's father's death effected change in all areas of her life.' - 'Effect' = verb --> the death caused change in Sally's life.
'The death of Sally's father really affected her'. - 'Affect' = verb --> The death had a significant impact on Sally.
You may already know all of this but I am trying to demonstrate that we couldn't really say, 'effect a friend'. That would mean 'to cause a friend'. You could say, 'Their perilous journey effected a lifelong friendship' but to 'cause a friend' in itself, in my view, is incomplete and meaningless. I would say that this slogan is grammatically incorrect and I think you raise a good point as to whether or not there is a play on words happening here.
I'm personally missing the point of the slogan. The only way it could make any sense to me is perhaps if the competition involves winning a camry in order to give it to somebody which would effect a friendship. However, this interpretation seems a bit stretched and, in any case, the word 'friendship' would be preferable to 'friend'. I wonder what was going on in the mind of the person who came up with the slogan - is there something clever that we're missing? (probably not!) or is it just poor English? (which in my opinion seems to be the case!)
I apologise for my final sentences (namely, "is there something clever that we're missing? (probably not!) or is it just poor English? (which in my opinion seems to be the case!)") as, in all honesty and despite my love of punctuation, I'm not sure where the question marks should be and I'm aware that the comments in parentheses do not constitute complete sentences. I'm not raising a question here I'm just letting you know that I'm aware of the errors and perhaps these sentences are ripe for editing.