grep -E '^[^0-9]*1234([^0-9]+1234)*[^0-9]*$' file.txt

Explanation

• ^[^0-9]*1234: find the first match of 1234, which may be preceded by non-digit characters.
• ([^0-9]+1234)*: there may be further iterations of 1234, but these must be separated from the first 1234 (and other 1234) by non-digit characters (hence use +).
• [^0-9]*$: match the entire line (with $). There may be non-digit characters after the final 1234 (but not necessarily, hence *).

EDIT

If 1234 must be delimited by spaces (or be at the beginning or end of the line), then use

grep -E '^([^0-9]* )?1234(( [^0-9]*)? 1234)*( [^0-9]*)?$'

Explanation

• ^([^0-9]* )?: there may be non-digit characters to start with, as long as they end with a space.
• 1234: find the first (required) match of 1234.
• (( [^0-9]*)? 1234)*: I'll work through the parentheses backwards. There may be (zero or more) further copies of 1234, but these must be preceded by a space, i.e. 1234. Before this space, there may be non-digit characters, which is fine as long as these are separated from the preceding copy of 1243 by another space, i.e.( [^0-9]*)?.
• ( [^0-9]*)?$: there may be non-digit characters to end with, as long as they are preceded by a space.

If I understand correctly, you want the 5th column to become the concatenation with space of all the 6 digit numbers in it.

Maybe:

perl -F'\t' -lape '
   $F[4] = join " ", grep {length == 6} ($F[4] =~ /\d+/g);
   $_ = join "\t", @F' < file

Or reusing your negative look around operators:

perl -F'\t' -lape '
   $F[4] = join " ", ($F[4] =~ /(?<!\d)\d{6}(?!\d)/g);
   $_ = join "\t", @F' < file

With awk:

awk -F'\t' -v OFS='\t' '
  {
    repl = sep = ""
    while (match($5, /[0-9]+/)) {
      if (RLENGTH == 6) {
        repl = repl sep substr($5, RSTART, RLENGTH)
        sep = " "
      }
      $5 = substr($5, RSTART+RLENGTH)
    }
    $5 = repl
    print
  }' < file

grep itself is not very adequate for the task. grep is meant to print the lines that match a pattern. Some implementations like GNU or ast-open grep, or pcregrep can extract strings from the matching lines, but that's quite limited.

The only cut+grep+paste approach I can think of that could work with some restrictions would be with the pcregrep grep implementation:

n='(?:.*?((?1)))?'
paste <(< file cut -f1-4) <(< file cut -f5 |
  pcregrep --om-separator=" " -o1 -o2 -o3 -o4 -o5 -o6 -o7 -o8 -o9 \
    "((?<!\d)\d{6}(?!\d))$n$n$n$n$n$n$n$n"
  ) <(< file cut -f6-)

That assumes that every line of input has at least 6 fields and that the 5th field of each has in between 1 and 9 6-digit numbers.