RFC 2132 (DHCP Options and BOOTP Vendor Extensions), section 3.8 says:
The domain name server option specifies a list of Domain Name System
[...] name servers available to the client. Servers
SHOULD be listed in order of preference.
"Should", not "Must", so, it depends on the client...
For example, Windows tries the first one, and falls back to the others if needed:
You can specify multiple servers for DNS resolution. Their priority is
determined by the order. If the first server isn't available to
respond to a host name resolution request, the next DNS server in the
list is accessed, and so on
Configuring TCP/IP networking
Same on Linux:
The algorithm used is to try a name server, and if the query times
out, try the next, until out of name servers, then repeat trying all
the name servers until a maximum number of retries are made.
RESOLV.CONF(5)