Retina, 23 bytes

(.).
1ドル1ドル$&
.
$*
M`.
0$

Try it online!

Explanation

Example input: 20378240

(.).
1ドル1ドル$&

Replace each couple of digits with the first digit repeated twice followed by the couple itself. We get 2220333788824440

.
$*

Convert each digit to unary. With parentheses added for clarity, we get (11)(11)(11)()(111)(111)...

M`.

Count the number of ones. (With the last two steps we have basically taken the sum of each digit) Result: 60

0$

Match a 0 at the end of the string. This is how we check for divisibility by 10. Final result: 1.

Retina, (削除) 23 (削除ここまで) 22 bytes

-1 byte thanks to Martin Ender !

(.).
1ドル1ドル$&
.
$*
M`
1$

Try it online!

Explanation

Example input: 20378240

(.).
1ドル1ドル$&

Replace each couple of digits with the first digit repeated twice followed by the couple itself. We get 2220333788824440

.
$*

Convert each digit to unary. With parentheses added for clarity, we get (11)(11)(11)()(111)(111)...

M`

Count the number of matches of the empty string, which is one more than the number of ones in the string. (With the last two steps we have basically taken the sum of each digit +1) Result: 60

1$

Match a 1 at the end of the string. We have multiplied digits by 3 and 1 alternately and summed them, for a valid barcode this should be divisible by 10 (last digit 0); but we also added 1 in the last step, so we want the last digit to be 1. Final result: 1.