In terms of animals humans tend to place more in their spheres of compassion, companion animals are fairly well-considered. But with pet ownership having gone up over the past few decades, this opens up a question about whether pets pose an ethical problem or if they can be part of a solution.
In Canada, where I currently live, pet food is a billion dollar business. In terms of cat food, sales were 655 million dollars in 2011 . With pet foods containing a significant amount of animal products (some more premium brands are ~90-99% meat-based, whereas others use plant-based "fillers"), it's clear that pets, specifically dogs and cats, have an effect on meat production in the United States and Canada and thus have a negative effect in terms of farmed animal suffering.
The question of exactly how much demand is affected falls outside of the scope of this post, but it's an intriguing question.
However, are individuals who have companion animals, or had one as a kid, more likely to be vegetarian?
A 2014 paper titled "Childhood pet ownership, attachment to pets, and subsequent meat avoidance. The mediating role of empathy toward animals" attempted to answer this question. Though the study was not longitudinal and is based on self-reported recollection of pet ownership, the results seem promising:
"... efforts to promote healthy pet ownership (among both existing and potential households) will not only pay off in terms of outcomes purely beneficial to the individual, but through greater meat avoidance, will also lead to outcomes that may be beneficial to society as a whole."
This is where the issue gets a bit uncertain. Does the positive meat reduction from pet ownership balance out pet food's contribution to farmed animal suffering? I think it's unlikely that carnivorous pets are a positive on balance [*3].
Notes and Sources:
A quick search returned a few numbers (these are numbers for Canada):
655 million dollars in cat food sales (including treats) in 2011. 
7.9 million cats in Canada in 2011. 
Which comes to about ~$83 spent on food and treats for one cat for each year. Not too unreasonable, and the numbers provide a bit of context into how large this market is. So it's not just a theoretical demand for meat, it is in fact quite tangible.
[*3] Though this conclusion doesn't take into account wild animal suffering, which is a large consideration.