Sure you can... I'm currently listening to Pink Floyd's "The Wall" in album order. All I listen to is complete albums and always play through in track/album order. I'm using the web interface and free version and there *is* an option on the playback bar to "Enable shuffle" but I don't use it...
I'm 100% anti Apple ecosystem... Even if I got it free I'd not use it.
I use Spotify free at work. It has almost everything I own (and that's over 1400 CDs) and lots of stuff I've always been curious about. There are complete albums from the 50s through to current - many I've been surprised...