Short answer
Technically yes, but the risk is not in the paper — paper is more reliable than a hard drive. The risk is in every node the data passes through during printing: clipboard, OS print queue, printer memory, ink-cartridge cache, network-printer server logs, cloud-syncing all-in-ones. A casual print can silently leak the private key to three or four places you weren't paying attention to.
The four leak channels
Clipboard. The instant you press Ctrl+C, Windows and macOS push to clipboard history. Tools like Alfred, Raycast, ClipMate retain recent entries. Cloud-clipboard syncing (Apple Universal Clipboard) replicates to every device on the same Apple ID.
OS print queue. Documents convert to PostScript or PDF spool files (the Windows system spool directory, or /var/spool/cups on macOS). These are supposed to delete after printing, but driver bugs or abnormal exits leave residue. Forensic recovery tools find them easily.
Printer firmware memory. Modern home laser printers carry 64-256 MB RAM; some retain the last few documents in NAND flash even after power-off. CBS News documented in 2010 that used office printers could be forensic-extracted to recover thousands of medical records. Same applies to your home device.
Network paths. Office network printers spool to a print server with audit logs. Wi-Fi printers like Brother and HP often back up jobs to vendor cloud for "remote print history." A consumer all-in-one with cloud print enabled has already transmitted the document outside your home network.
If you must print
Use a fully USB-connected printer (no Wi-Fi, no Ethernet). Print from an offline computer that has never been connected to the internet, or boot from a Tails USB. Factory-reset the printer immediately after, clearing all logs. Best alternative: hand-transcribe to steel. Steel plates (Cryptosteel, Billfodl) cost $60-80 and skip the entire digital surface.
Further reading: Five ways to store a seed phrase.