Do the scholastic sects say that chan practice is something separate from themselves? Dogen famously said that there are no Buddhist schools, and the idea there is [this or that Buddhist school] is the creation of demons, etc. [Dogen's Eihei Koroku, discourse 7.491, reads:]


  The Buddha Dharma fundamentally has no outer name or form. Later
  people falsely established many random names. Althogh facing the wall
  at Shaolin resembled [dhyana], do not call it Zen School and misguide
  sentient beings.


First, is Dogen saying that Zen [which is misguiding] is nothing separate from scholastic "sects", and if so, is he right?

Second, what do the more scholarly schools - whether Theravada, Mahayana or Vajrayana - say about Zen?
Remember the concentration division of the Eightfold Noble Path consist of Right Effort, Right Mindfulness, Right Concentration.

The Noble Eightfold Noble Path did not specify a particular practice for obtaining mindful concentration as long as long as they are consistent with the teachings. You can obtain Right Concentration from Sitting Meditation "Zazen" or you can chant sutras, or you can do walking meditation. In fact for the Chan/ Zen practitioner they aspire to maintain Right Effort, Right Mindfulness and Right Concentration in every moment, in every thought. Some  practices are easier than others to obtain concentration however, that's why sitting meditation is generally fundamental since it avoids distractions.

To summarize:

Right Effort


  "And what, monks, is right effort?
  
  [i] "There is the case where a monk generates desire, endeavors,
  activates persistence, upholds &amp; exerts his intent for the sake of the
  non-arising of evil, unskillful qualities that have not yet arisen.
  
  [ii] "He generates desire, endeavors, activates persistence, upholds &amp;
  exerts his intent for the sake of the abandonment of evil, unskillful
  qualities that have arisen.
  
  [iii] "He generates desire, endeavors, activates persistence, upholds
  &amp; exerts his intent for the sake of the arising of skillful qualities
  that have not yet arisen.
  
  [iv] "He generates desire, endeavors, activates persistence, upholds &amp;
  exerts his intent for the maintenance, non-confusion, increase,
  plenitude, development, &amp; culmination of skillful qualities that have
  arisen: This, monks, is called right effort."


http://www.accesstoinsight.org/ptf/dhamma/sacca/sacca4/samma-vayamo/index.html

Right Mindfulness


  "One is mindful to abandon wrong view &amp; to enter &amp; remain in right
  view: This is one's right mindfulness...
  
  "One is mindful to abandon wrong resolve &amp; to enter &amp; remain in right
  resolve: This is one's right mindfulness...
  
  "One is mindful to abandon wrong speech &amp; to enter &amp; remain in right
  speech: This is one's right mindfulness...
  
  "One is mindful to abandon wrong action &amp; to enter &amp; remain in right
  action: This is one's right mindfulness...
  
  "One is mindful to abandon wrong livelihood &amp; to enter &amp; remain in
  right livelihood: This is one's right mindfulness..."


http://www.accesstoinsight.org/ptf/dhamma/sacca/sacca4/samma-sati/index.html

Right Concentration


  "Now what, monks, is noble right concentration with its supports &amp; requisite conditions? Any singleness of mind equipped with these seven factors — right view, right resolve, right speech, right action, right livelihood, right effort, &amp; right mindfulness — is called noble right concentration with its supports &amp; requisite conditions."


http://www.accesstoinsight.org/ptf/dhamma/sacca/sacca4/samma-samadhi/index.html

As long as the Noble Eightfold Path is being practiced, mindful concentration is possible and therefor the Jhanas also known as Chan or Zen is possible. Therefore the myriad practices of Buddhism lead to the same thing and there is no separation. You can scrub clean the floor and have mental concentration to experience Joy and Peace in your heart. Or you can chant sacred scriptures while performing complex mudras.

In theory, the Noble Eightfold Path must be practiced by every school of Buddhism and hence 'Chan/Zen' is practiced by every schools of Buddhism whatever their names maybe. However, as it tends to happen there are monks and schools who don't know what they are doing and spend their time debating philosophical concepts in the scriptures or running a temple like a business and not cultivating themselves and not practicing the Dharma. Even within the Chan/Seon/Zen school in China/Korea/Japan there are people who lost sight of what 'Zen' actually means and engaged in pointless philosophizing. As long you know how it work you can see the practices everywhere and not be confused by surface appearances.