Then I would propose to use the IntegerString combined with StringContainsQ A 1000000 digit number to string convertion takes 0.13 Seconds to convert. Using StringContainsQ is almost instantanous.

(s = IntegerString[2^4000000, 10];
  StringContainsQ[s, "0"];) // AbsoluteTiming

takes 0.136 seconds

The highly improbable no zero 1000000 digits

range=CharacterRange["1","9"];    
s2 = RandomChoice[range, 1000000] // StringJoin;
StringContainsQ[s2, "0"] // AbsoluteTiming

is False within 0.00009 seconds. Pretty impressive I would think

a 500000 digit number

(s = IntegerString[3^999999, 10];
  StringContainsQ[s, "0"];) // AbsoluteTiming

in 0.049 seconds

DigitCount[3^10232222, 10, 0] // AbsoluteTiming

takes 1.7s in my computer vs 0.003s for

n = 3^10232222;
AbsoluteTiming[While[! Divisible[n = Quotient[n, 10], 10]]]

I don't need the number of 0 in the number really just if theres any 0 in it.

DigitCount[3^10232222,10,0]//AbsoluteTiming

In 0.8 seconds fast enough? I think it's fast for numbers having a zero somewhere at the beginning

n = Prepend[Table[RandomInteger[{1, 9}], 400000], {1, 0}] // Flatten //
    FromDigits;

runs in 0.03 seconds but your procedure takes very long (aborted)

I am not sure what you are trying to do with your code, it does not seem to work. Perhaps:

MemberQ[RealDigits[N[Pi, 10]][[1]], 0]

False

MemberQ[RealDigits[N[Pi, 50]][[1]], 0]

True

or maybe to see where 0s are:

Position[RealDigits[N[Pi, 100]][[1]], 0]

{{33}, {51}, {55}, {66}, {72}, {78}, {86}, {98}}