No. While improper priors can be okay for parameter estimation under certain circumstances (due to the Bernstein–von Mises theorem), they are a big no-no for model comparison, due to what is known as the marginalization paradox.
The problem, as the name would suggest, is that the marginal distribution of an improper distribution is not well-defined. Given a likelihood $p_1(x \mid \theta)$ and a prior $p_1(\theta)$: the Bayes factor requires computing the marginal likelihood:
$$p_1(x) = \int_\Theta p_1(x \mid \theta) p_1(\theta) d \theta .$$
If you think of an improper prior as being only known up to proportionality (e.g. $p_1(\theta) \propto 1$), then the problem is that $p_1(x)$ will be multiplied by an unknown constant. In a Bayes factor, you'll be computing the ratio of something with an unknown constant.
Some authors, notably E.T. Jaynes, try to get around this by defining improper priors as the limit of a sequence of proper priors: then the problem is that there may be two different limiting sequences that then give different answers.