Yes. Access to objects stored in S3 accessed via a Signed URL work fine without a NAT Gateway or IGW if you have a VPC Endpoint for S3 configured and in use the the associated Route Table for the subnet.
Easy to verify by quickly building a VPC with Public & Private Subnets, bastion instance in Public Subnet, Isolated Instance in Private Subnet. Configure VPC Endpoint for S3 to be used by Private Subnets. Generate a signed URL for an object and try to use wget to retrieve it. Works fine.
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