I don't think being a PR of old will prevent CIC from starting to process your FSW application because checking if a PR applicant is already a PR is simply not the first thing that would come to their mind.
Your applying for a PR travel document simultaneously may not even be known to them as you are doing that through a different office. However, maybe you'd want to delay it until they ask.
There was someone on here recently who applied under FSW with an old PR without even knowing about it and they processed his application but at some stage got back to him and told him that he must renounce the old PR for his application to continue. They even sent him a form for a travel document to fill out which baffled him as he looked at it and saw that it was an application to actually keep his old PR but the form for PR TD is also used by many office in order to renounce or to force a decision on your status.
Your applying for a PR travel document simultaneously may not even be known to them as you are doing that through a different office. However, maybe you'd want to delay it until they ask.
There was someone on here recently who applied under FSW with an old PR without even knowing about it and they processed his application but at some stage got back to him and told him that he must renounce the old PR for his application to continue. They even sent him a form for a travel document to fill out which baffled him as he looked at it and saw that it was an application to actually keep his old PR but the form for PR TD is also used by many office in order to renounce or to force a decision on your status.