Yes, basically by using stranded CAT5e you will be making up a "patch" cable with rj45 plugs. Solid core is best suited for use with rj 45 sockets where one would use two short ethernet cables also: one from the modem to the downstairs rj45 socket and the other for the upstairs rj45 socket to the router.
I've used a 20 metre rj45 "patch" ethernet cable for testing a gigabit LAN setup prior to installing solid core CAT5e and it worked OK. For your setup, where initially gigabit speeds wont be needed for FTTC, a long patch cable should be fine.
BTW. Because FTTC is now available to my neighbours and myself I've got all the kit ready to go: solid core, 4 pair, 100% copper CAT5e, rj45 sockets, filtered NTE5 faceplate, NTE5 master socket etc. - may need all that stuff since contract installers may not do a good job. Personally I'm not interested in getting vdsl myself at the moment because a 13Mbps ADSL2+ sync is adequate for my needs but I'm certain some of my neighbours will
Edited by 4M2 (Sat 26-Oct-13 00:11:30)