HDMI (which has nothing to do with Blu-ray other than a BD player requires using HDMI) will not improve the audio or video of a DVD. All HDMI does is provide a single cable connection between the player and the display, instead of the three separate audio/video cables previously used. It does keep the video and audio signal in the digital realm, but that in itself can't "improve" the signal. It can potentially keep stray electronic "noise" from disrupting the signal, but that's really not something that happens much.
Your Roku of course requires an HDMI connection, unless you have an older player with analog outputs. Since every Roku player is capable of higher resolution video than any DVD player, HDMI certainly provides the highest quality video signal compared to the old analog connection. Also be aware there are some DVD players that offer "upscaling" using an HDMI cable. However, while it might look a bit better than the analog video, it's being upscaled and the higher quality is artificial. With a Blu Ray disc, you are starting with a higher quality signal and it's not artificially being enhanced.
One additional comment about HDMI audio. Since almost every DVD is encoded with Dolby Digital audio, using an HDMI connection does keep that digital audio intact all the way to the TV. It's possible to have slightly better sounding audio if you keep that within the digital realm all the way to the audio amps in the TV. If you're using an AVR, then you can absolutely get better audio with an HDMI connection, even from a DVD.
