If I buy one of the DVD players that upconverts to 1080i, does that require use of the HDMI port on my TV?

I have an OPPO DV 970-HD and it only upconverts to 1080i with HDMI. It will only go to 480i/480p through component (I believe there might be hack to change this). I am not sure what other players require.

To quote their website:
Multiple high definition video formats through HDMI and component outputs*: NTSC: 480i/480p/720p/1080i; PAL: 576i/576p/720p/1080i (* Component output for CSS-encrypted DVD discs (almost all commercially pressed DVD discs) is limited to 480i/480p only.)

Yeah, you pretty much need HDMI for upconversion due to studio paranoia. I think there may be one or two rare no-name component upconverting players, but good look on getting those.

So would it be worth it to get an HDMI switch? I use HDMI for my DirecTV, and have no intention of changing it....and my TV only has one HDMI port.

It would depend on the TV too. Mine (Sony 60A2000) can accept up to 1080i through component, but accepts 1080p through HDMI only. So along with the player stats, check your TV owner's manual too, it should tell you what it accepts through what. At any rate, yeah, an HDMI switch wouldn't be a bad idea.

Is there any loss of quality with an HDMI switch?

I don't have one, but I haven't heard of any noticable loss by using such a switch.