Most likely no.
The pickling process typically boils the bottles to a point that kills any organisms in order to prevent spoilage -- this includes the seeds.
(I say "most likely" because some pickling processes are done cold and use a more natural sort of fermentation. But unless you got your pickled peppers at a very traditional sort of shop or from an old-school farmer at a farmers' market, they've been boiled and the seeds will not grow.)
Beyond the processing issue, even if the seeds were viable, if your peppers happen to be a hybrid variety, you won't get plants that produce the same fruit.
Considering that you can get 100 viable jalapeno seeds for under US$2, it's really not worth bothering trying to salvage the debris off the bottom of the pickle jar...