Did Darwin ever reach the conclusion that selection will remove variation?
After reading your question, I had a vague memory that this subject was indirectly touched upon in "On the Origin of Species", so I did some text searches (in this pdf version I found online). From what I can see, Darwin never used the technical term 'variance' (I don't know how old this use of the word is), but 'variability' is often used, both with regard to accumulated variation but also meaning variation between individuals within a population. 

All-in-all, I could not find clear support for the idea that selection will decrease the amount of variation. However, there are number of passages where the subject of variation vs selection comes up (often indirectly), but, to me, these just as often (most often?) indicate that Darwin saw no risk that selection would reduce variation as the opposite. Here are the most interesting passages I could find (searching for combinations of 'variab*', 'selection', 'decrease' etc), with page references referring to the pdf version and a short comment below each quote:


  A large number of individuals,
  by giving a better chance for the appearance within
  any given period of profitable variations, will compensate 
  for a lesser amount of variability in each individual, 
  and is, I believe, an extremely important
  element of success.
  (p. 44)


This is clearly discussing amounts of variation within species, where large numbers can compensate for a smaller amounts of standing variability, by increasing the chance of advantageous mutations.


  Nothing can be effected, unless favourable variations
  occur, and variation itself is apparently always a very
  slow process. The process will often be greatly retarded 
  by free intercrossing. Many will exclaim that
  these several causes are amply sufficient wholly to
  stop the action of natural selection. I do not believe
  so. On the other hand, I do believe that natural selection 
  will always act very slowly, often only at long
  intervals of time, and generally on only a very few
  of the inhabitants of the same region at the same time.
  (p. 103)


Not directly related to selection vs variation, but deals with the rate of evolution vs amount of variation.


  But what here more
  especially concerns us is, that in our domestic animals 
  those points, which at the present time are undergoing 
  rapid change by continued selection, are
  also eminently liable to variation. Look at the breeds
  of the pigeon; see what a prodigious amount of difference 
  there is in the beak of the different tumblers,
  in the beak and wattle of the different carriers, in the
  carriage and tail of our fantails, &amp;c., these being the
  points now mainly attended to by English fanciers.
  Even in the sub-breeds, as in the short-faced tumbler, 
  it is notoriously difficult to breed them nearly
  to perfection, and frequently individuals are born
  which depart widely from the standard. There may
  be truly said to be a constant struggle going on between, 
  on the one hand, the tendency to reversion to
  a less modified state, as well as an innate tendency
  to further variability of all kinds, and, on the other
  hand, the power of steady selection to keep the breed
  true. In the long run selection gains the day, and we
  do not expect to fail so far as to breed a bird as coarse
  as a common tumbler from a good short-faced strain.
  But as long as selection is rapidly going on, there
  may always be expected to be much variability in
  the structure undergoing modification.
  (p. 141)


This is maybe the most interesting passage, which to me indicates that he saw little risk that selection could/would limit variability (see especially beginning and end).


  For forms existing in larger
  numbers will always have a better chance, within
  any given period, of presenting further favourable
  variations for natural selection to seize on, than will
  the rarer forms which exist in lesser numbers. Hence,
  the more common forms, in the race for life, will tend
  to beat and supplant the less common forms, for
  these will be more slowly modified and improved.
  (P. 162)


Also on limitations for variation that selection can act on, and the value of large populations.


  ... firstly, because new varieties are
  very slowly formed, for variation is a very slow process, 
  and natural selection can do nothing until
  favourable variations chance to occur, and until a
  place in the natural polity of the country can be better 
  filled by some modification of some one or more
  of its inhabitants. And such new places will depend
  on slow changes of climate, or on the occasional immigration 
  of new inhabitants, and, probably, in a still
  more important degree, on some of the old inhabitants 
  becoming slowly modified, with the new forms
  thus produced and the old ones acting and reacting
  on each other.
  (p. 163)


On the limiting nature of variation, but does not connect selection to decreased variation.


  It cannot be asserted that organic beings
  in a state of nature are subject to no variation; it cannot 
  be proved that the amount of variation in the
  course of long ages is a limited quantity; no clear
  distinction has been, or can be, drawn between spe-
  cies and well-marked varieties.
  (p. 425)


On variation over the long run.

These are the most interesting sections I found on the subject from my (quick and limited) searches. I hope you find them useful. However, this is only based on the first edition of "On the Origin of Species", and it is possible that it is is modified in later editions or that he touches upon this in his other writings. However, when looking at these particular passages in the sixth edition, I cannot see a major change in his thinking.