No, no it can not. Take the question to its logical extreme to test the validity of the basic hypothesis.

Say the President negotiated and the Senate ratified a treaty that, ummmm, lets pick something EXTREMELY offensive from recent history for illustrative purposes, made enslavement of all persons with any African heritage and murder of all Jews mandatory. Would that then grant Congress the power to pass laws to implement said treaty? Of course not.

OK, let’s pick a lesser, since there’s no murder or enslavement, but still serious, example. What if the President negotiated (say with Egypt and Saudia Arabia) and the Senate ratified a treaty to ban those “evil” fundamentalist Christians from practicing their Faith, while making the Islamic Faith the one true religion of the US. Would that then override the Constitutional provisions on the matter and grant the Congress the power to pass laws to enforce said treaty? Of course not.

OK, lets go for an even lesser case. What if the President negotiated and the Senate ratified a treaty that banned the private ownership of small arms. Would that grant the Congress the power to pass laws to confiscate privately owned arms? Of course not.

Sometimes I think all that fancy legal education of Lawyers messes up their ability to engage in common sense consideration of questions. Take the proposal or principal at hand, then take it to its fullest extreme to see if it withstand scrutiny. Using the above examples, the principal that Congress can increase it’s legislative power via treaty is clearly falsified, since if the principal held, then the above examples would also hold, making the Constitution and Bill of Rights a moot point – subject to the whim of 1 + 67 people. Anyone with more than two functioning brain cells knows this isn’t the bargain that the Founders made.