Sure. See MythTV and a knoppix derivative KnoppMyth.
Is there any way that you can use Linux as a media center like you can with media center edition. Or I was thinking that maybe I could record TV and then have it work as a server that could be used to watch the shows later on on other computers. Is there anyway that I could do that?
Sure. See MythTV and a knoppix derivative KnoppMyth.

New Barebones Supermicro 5019D Server, 4C/8T Xeon D-2123T, 1U Rackmountable, 10G
$449.99
HP Proliant MicroServer Gen 8 2.23GHz Xeon 16GB RAM NO SSD
$249.99
$280.00
Supermicro CSE-937 3U Storage Chassis No CPU No HDD No Ram Tested & Reset
$129.99
Supermicro SuperServer E300-15 - SYS-e300-9C - 16GB RAM 240GB Samsung SSD
$239.00
SuperMicro 4U CSE 847 36 Bay LFF Barebone 2x 1280W w/ 2x Bays 2.5 Rear w/Trays
$499.99
1U Edge Firewall Server X11SCW-F Xeon E-2174G 0 RAM M.2 NVME 3x PCI-e 2x PSU X
$175.00
Supermicro 2U X10DRU-i 2x E5-2680 v3 2.5ghz 32gb Ram 240gb SSD 2x GPU *READ*
$369.99
Supermicro E300-12C Mini 1U Barebone X12SCV-LVDS LGA1200 SNK-P0073A4 w/ Adapter
$225.00
Nasuni NF-50 Supermicro Server, Atom CPU C2558, @ 2.40GHz, 8GB RAM-No HDD/OS/AC
$250.00