With everything packed to maximize horizontal dependencies (everything manually assigned locations and every LUT dependent on the output from a register in a LAB immediately to the left of it), the most direct left-to-right links I see crossing a single boundary is 14. Not sure if that's a hard limit, however (the fitter is still somewhat reluctant to use them - most of the time it won't even use all 14, would route 10 or 11 directly, and send the rest via a Rx/Cx interconnect.)
Out of 4 registers in each ALM, 2 are only able to drive direct left-to-right links, and the other 2 are only able to drive right-to-left links. So, the maximum width of any pipeline that can be implemented using only local routing is, at most, 20 bit per LAB.