Is it really a comcoin?

Python 2, 62 56 49 bytes

lambda n:max(`n`)<"2"and 0x5d75d750>>int(`n`,2)&1

Credit to @Sp3000 for the max trick to ensure binary digits.

JavaScript (ES6), 38 27 bytes

n=>2641714512>>'0b'+n&n<1e5

Port of @orlp's Python answer, except that JavaScript's precedence and weak typing allows me to shift the integer even if it's not valid in base 2, and then bitwise and it with the boolean. Returns 0 or 1 as appropriate. Note that I'm not using @orlp's constant any more, instead I'm assuming the following list of comcoins is valid:

100
110
1000
1010
1011
1100
1110
10000
10010
10100
10101
10110
11000
11010
11011
11100
11111

Edit: Fixed to check the length of the comcoin, since JavaScript's shift operator works modulo 32.

MATL, 20 bytes

n6<G50<9:Q"G@ZAZp~vA

Input is a string.

Try it online!

Explanation

n6<    % take input implicitly. Is length less than 6?
G50<   % push input again. Array that contains true for digits less than 2
9:Q    % push array of bases: [2,3,...,10]
"      % for each
  G    %   push input again
  @    %   push current base
  ZA   %   interpret input as if it were in that base, and convert to decimal
  Zp~  %   true for composite numbers
  v    %   concatenate vertically all results up to now
  A    %   true if all results were
       % end for each implicitly
       % display implicitly