is it possible that constant storms would be present between the day and night sides?
So long as there's an atmosphere, there kinda has to be some flow of air. Modelling how violent it would be is hard, but I think you can justify storm-strength winds.
would the storms extend all the way around the planet or would they die out towards to poles?
If you did get a complete ring of bad weather around the he world at the edge of the day-side, you could give the phenomenon the splendid name of Terminator Storm.
There's a chance that you won't get this at all, though.
Venus isn't quite tidally locked, but its rotation is so slow that it may as well be. Its atmosphere on the other hand undergoes super-rotation, where it rotates around the world considerably faster than the planet itself rotates. Titan is another world which is tidally locked whose atmosphere apparently superrotates too.
This is potentially a good thing for tidally locked worlds as it would redistribute heat around the planet quite effectively, preventing the atmosphere from freezing out on the dark side and increased thermal escape on the light side leaving a mostly or entirely airless world.
This gives you continuous equatorial wind, but where the storms would end up I'm much less sure. We know that Venus has lightning, mostly on the light side at low latitudes, so clearly storms of some kind can and do arise even in that atmosphere. A cooler and wetter world should be able to support storms more like those we experience on Erath.
Note that on Venus, the winds mostly travel around the world (zonal flow) with a much smaller north-south component than winds on Earth do... you don't get much flow over the poles on either planet. What you do get on Venus are vast, apparently permanent polar storms:
They are giant hurricane-like storms four times larger than their terrestrial analogs. Each vortex has two "eyes"—the centres of rotation, which are connected by distinct S-shaped cloud structures.
and if that doesn't enthuse you, I don't know what will.