Nope. The House has to pass funding. If they don’t, the Senate can’t change that. Hence the phrase “The House holds the purse strings.”
This was described as a vote to “defund”, implying most likely that the funding was previously approved. In which case the Senate and President’s signature are needed.
The other possibility, is that it’s an appropriation bill, but that does still take the Senate and President’s approval. Without that the entire appropriation bill goes down, and so far the house has been too gutless to shut the government down.