Noooooo! Not only would you be exposing your body to potential infection as well as to dangers inherent in using non medical-grade saline (an endless array of potential impurities and concentration disparities), but, you'd also be performing an ineffective technique.
Unless the deeper, reticular network of veins supplying the spider veins are treated at the same time, the spider veins will likely recur over time. Furthermore, if one or more of the valves within the deep veins is incompetent, this problem must be fixed before any lasting results from spider vein treatments can be achieved.
Finally, (hypertonic) saline injections are painful. There are better options for sclerotherapy solutions (i.e. foam preparations of sodium tetradecyl sulfate and/or polidocanol) that are not only significantly less painful, but, also are just as - if not more - effective than hypertonic saline.
On a side note, despite the popularity in the past of using hypertonic saline as the solution ("sclerosant") in sclerotherapy, it is actually not FDA-approved for this purpose. Both sodium tetradecyl sulfate and polidocanol are FDA-approved for this indication.