It really depends...
Modern browsers typically restrict the number of HTTP connections with the same domain to six, as defined in the HTTP specification (RFC2616). Older browsers, on the other hand, often only allow two connections per domain.
Reference
So, if there are no pending requests in your situation, all three requests can be triggered simultaneously. It's important to note that the connection limit applies to each domain individually. If your three Ajax calls are to three different domains (such as different CDNs), they are likely to be triggered simultaneously without waiting for responses.