Yes they will. Chrome's http2 tag is a great way to explore how http2 requests are emitted: chrome://net-internals/#http2.
For the requests emitted by SSE, you should see something like:
HTTP2_SESSION_SEND_HEADERS
--> exclusive = true
--> fin = true
--> has_priority = true
--> :method: GET
:authority: h2.example.org
:scheme: https
:path: /demo_sse.php
accept: text/event-stream
cache-control: no-cache
referer: https://h2.example.org/
accept-encoding: gzip, deflate, sdch, br
accept-language: en-US,en;q=0.8,fr;q=0.6,es;q=0.4
--> parent_stream_id = 0
--> priority = 1
--> stream_id = 7
As you can see in this example, the browser sent the request on stream id 7, re-using the connection it had to fetch the html.