Is there independent evidence that physical computing improves engagement
There are many academic articles reporting high engagement, especially among students underrepresented in computing, using physical computing. https://scholar.google.com/scholar?q=physical+computing+education . Most of them lack a controlled study design. That doesn't mean they don't provide evidence however. For example, from Peppler 2013:


  The capacity for e-textiles to diversify participation was first
  documented by Leah Buechley and Benjamin Mako Hill,2 who discovered
  that while men created the majority of traditional Arduino projects
  posted on Vimeo, YouTube, Flickr, and other sites (85 percent), women
  created most of the LilyPad Arduino projects (65 percent). What is
  striking about this comparison is that both types of projects share
  the same microprocessor and are programmed in the same language. The
  researchers suggested that the gender discrepancy could be due to some
  combination of the tools and materials used (insulated wire versus
  conductive thread to make connections between components), the
  construction practices employed (soldering versus sewing), and the
  nature of the products (robots versus interactive quilts).
  
  To understand whether changing these factors could significantly alter
  classroom culture in a similar way, we implemented a series of
  e-textile experiments in middle school settings where we closely
  observed how gender dynamics played out. From videotaped observations
  of subjects working in mixed-gender pairs, we found that both boys and
  girls equally engaged in e-textile activity, as evidenced by body
  language, gaze, talk-on-task, and other indicators, but girls tended
  to play a greater leadership role. The projects were positioned in
  front of the girls 81 percent of the time; the girls also spent 58
  percent of the time directing activity, troubleshooting, and deciding
  next steps and made only 39 percent of the requests for help from
  teachers and peers. We found that this early leadership was predictive
  of having more sophisticated command of the technology in subsequent
  projects, requiring less troubleshooting and assistance from others.


That said, probably wise to heed the central advice of Kicking Butt in Computer Science: abandon gender difference as the underlying theory in what works, and emphasize instead a high value on diverse interests and on applications that positively impact people's lives.