Yes, your Roku will play media from a NAS (via DLNA). However, there are two caveats. You either have to have your media in a format that the Roku can play, or the file requires transcoding. Many NAS devices don't have the computer horsepower to transcode HD video. Basically, your media needs to be in the MKV or MP4 container, with H.264/MP4 video ( the 4K models also support H.265) and the audio needs to be AAC or AC3/Dolby Digital. It will also pass DTS core audio via HDMI, but you have to have something that can decode DTS, like an AVR, in the HDMI chain. Just so you know, virtually all DVDs will contain MPEG2 video, which Roku does not support (except for the TV models). Blu Ray movies are usually H.264, but I've encountered a couple with VC-1, which again Roku will not play. You can use a program like Handbrake to convert any non-compatible videos.
You could also install a DLNA server on a computer and stream the media files from the NAS through it. However, that puts a larger strain on your network. But most computers nowadays can perform transcoding without much effort.
Nvidia Shield, Roku Stick (3600), Ultra (4640), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.