No — the message box in a conversation has no attach button, so chat carries text only.
Files belong to the work itself, not to the chat. As a buyer, use the Product images and Product documents fields under each product line in the demand wizard — drawings, spec sheets and reference photos go there. As a supplier, use the Offer Documents section while you build your offer; that section is for files covering the whole offer, such as a cover letter, catalogue or company certificate.
Keeping files out of chat works in your favour: a file attached to a demand or an offer never gets buried in the message thread, it is clear which line item it belongs to, and everyone with access to that demand sees the same file.
A conversation is tied to one demand only, as the note under the chat window states. Send a short message telling the other side which file you added, and use Invite teammate to bring a colleague from your own company into the same conversation.
Also asked as: Can I attach a file to a message? · Can I send a photo in chat? · Can I share a PDF in the conversation? · Where is the paperclip button in chat?