Really, the answer has nothing to do with if certain web servers support HTTP 1.0, it depends if websites do.
With HTTP 1.0 there are no headers, including the host header, and therefore no virtual host capability (one website per IP address).
So any website that has more than one domain/hostname on a single IP will NEED the HTTP/1.1 'host' header to work at all.
Therefore, if you want your client to work with arbitrary websites, no, you can't do it, it won't work with all websites.
If there are specific websites, then... well you can test those to see if they will honour the HTTP 1.0 request, and if it does or not will depend on the web server AND its configuration.
You have to accept that if you have a specific set of destination websites that work they could stop working later too remember.
Edit (following question edit):
Since you control the server side PHP you control the content, but still not the web servers behaviour as such. Your host MIGHT be providing only your web content / web site at the IP address pointed to by your host/domain name, and in that case HTTP 1.0 MIGHT work... but if there are multiple host/domain names hosted on a single IP by the web server then it almost certainly won't work, and if it does work in either case then it COULD stop working at a later time.