Hi @the_dummy,
I agree on fastqc. To answer your question, not necessarily. It may depend on the prep kit and where are sequencing adapters. In my experience, the length of 250 bp includes everything, sequencing adapters (depending on kit ), barcodes as well as PCR primers and low-quality tails. Hence, for me when I saw 250 bp it means these are as raw as possible (for a 2x250 bp MiSeq run at least)
Cheers