Yes, but doing it intentionally isn't as simple as one might think. First, BGP generally prefers the shortest path and yours is going to be a little long, so unless the best original path is very long you need on some transit provider to use policy-based routing and trust you as transit. Second, if you want the traffic to pass through your hardware you have to have sufficient bandwidth, otherwise you'll just trigger packet loss and disrupt service (fine if disruption is your goal, not so fine if you want the traffic to pass through your hardware). Third, some people use signed routes, which also complicates your job.