No, the 4 bit checksum does not provide any extra security in this sense.

The 4 bit checksum is generated deterministically from the 128 bit entropy. The same 128 bits of entropy will always produce the same 4 bit checksum. So although a 12 word BIP39 seed phrase does encode 132 bits of data, there are not 2¹³² possible valid seed phrases. For every 132 bit seed phrase, there are 2⁴ possible combinations of the 4 bit checksum, but only one of them will be valid. Given that, 2¹³² / 2⁴ = 2¹²⁸.

If you want more than 128 bits of entropy in your BIP39 seed phrase, then you need to use more than 12 words, with the most common alternative being 24 words, which provides 256 bits of security with an 8 bit checksum.