Preparing a fresh bag of spinach: To Stem or Not To Stem
In my experience, stems can be rather stringy even after cooking. Likely varies by time of year, age/size of leaves, soil type, cultivar etc.
Best adivice is probably to check a few stems (raw, steamed, whatever) and see.
I always cut stems off at the base of the leaf, and have yet to have a complaint about the stem bits within the leaves.