Kind-of, sort-of. The weakness of ECB mode is the lack of interaction between blocks that causes identical plaintext blocks to produce identical ciphertext blocks. This leads to an attack sometimes termed the Tux attack where the identification of identical ciphertext blocks reveals information about the overall plaintext.
This can apply at the language level. If our plaintext is English language encoded in ASCII then for DES we have plaintext blocks distributed roughly according to the octagram frequency of English and for AES the hexadecagram frequency. These are both quite weak statistics as the space of possible octagrams and hexadecagrams is large (though still significantly smaller than the input space of the block ciphers, and significantly non-uniform). However, given a very large or very structured corpus, it is possible to obtain some information from repeated blocks.
This is particularly relevant when ECB mode is used to encrypt databases so that they remain searchable. I have one exercise that I sometimes present to high schoolers of an encrypted database with several repeated values and based on a well-known set of information. They are often able to recover 60-80% of the database entries based on the repeats and knowledge of some of the information.