I'm not familiar with DVB-C cards but it's unlikely.
Unless you have/get a dual tuner card, multiple tuners are the only way of watching one whilst recording another.
You'll be happy to know it's not an issue to mix and match the different DVB tuners. Using two of the same tuner can take some setting up though. The lads in the DVB-C-S-T room should be able to guide you further with regards to software, non-conflicting hardwares etc.
Also there is an issue with the DVB-T2 not being out yet; no one knows how much they are going to cost. Early adopters could well end up paying over £100...
Anyway, as you've got your DVB-C tuner here is a £400 HTPC PC, which should have enough grunt to record 2 channels whilst watching an HD video:
CPU:
AMD Athlon II X4 620 2.6GHz AM3 Retail Boxed Processor - Ebuyer
Mobo:
MSI 785GM-E51 785G Socket AM3 DVI VGA HDMI Out 8 channel audio mATX Motherboard - Ebuyer
DDR3:
Kingston 4GB (2x2GB) DDR3 1333MHz i5 Memory Kit CL9 1.5V - Ebuyer
GFx:
XFX 9600GT 512MB DDR3 DVI HDMI HDCP PCI-E Graphics Card - Ebuyer
HDD:
Samsung HD103SJ Spinpoint F3 1TB Hard Drive SATAII 7200rpm 32MB Cache - OEM - Ebuyer
Optical:
Samsung SH-S223 22X DVDRW/RAM/DL Serial ATA Black Bare Drive - OEM - Ebuyer
PSU:
Corsair 400W CX PSU - 12cm Fan 80Plus Certified Efficiency 6x SATA 1x PCI-E - Ebuyer
Case:
Coolermaster Elite 330 Black Mid Tower Case - No PSU - Ebuyer
You could probably swap out the graphics card for a blu-ray drive as the motherboard has HDMI out built in. However, you will 'lose' some system memory to the onboard graphics doing so.
Suggested future upgrades:
BD reader - the BD/HDDVD combos have been discontinued.
DVB-T2 tuner
Move boot partition to a seperate (smaller) hard drive.