No. I believe the only DSLR type cameras that can capture video are the Nikon D90 and the Canon 5D mark II.
Also, the forthcomming Panasonic GH-1 will have video. While this is not technically a DSLR because it doesn't using a optical reflex finder, using an eye level electronic finder instead, it does compete more with DSLRs than with "superzoom" P&S models since it uses interchangeable lenses and isn't burdened with the slow and imprecise motorized zooming mechinisms found in P&S cameras.
Although the xsi does not natively support video recording, you can download some software that will let you if you don't mind manual focus and being tethered to your computer. Çàïèñü âèäåî çåðêàëüíûìè ôîòîàïïàðàòàìè Translated version: Translated version of http://valexvir.narod.ru/