Sounds viable.
On the water...
I think your read that your motion doesn't matter is right. It's not analogous to the ineffective method of pointing a fan (from the stern) at the sails because... well, magic. In real life mounting a fan at the stern and pointing it at the sails doesn't work (well...1) because of the "reaction force" generated when the air is pushed forward.
But this spell clearly doesn't create a reaction force: the spell description contemplates pushing creatures away from the caster, but doesn't call out any "pushback" the caster feels. (Because he doesn't. Because magic.) So then "a line of strong wind... blasts from you." The plain reading of wind blasting from you is to say that "the air near you moves with some speed relative to you." You stand at the stern, look at the sails, and magically air behind the sails starts hitting them as a strong breeze emanates from you.
(How strong? The spell description gives us creatures in the area having difficulty walking (2'->1' typical "difficult terrain" rules). I equate this with the descriptor "effort needed to walk against the wind" given in the Beaufort Scale in the entry for "high wind, moderate gale, near gale." But the description also calls it a "strong wind," so perhaps we should look at the weaker Beaufort "strong breeze." Even then, it's 21-27 kts, or 35-46 fps.)
Now, hopefully you were running when you cast the spell, and you've just given yourself a significant boost. How significant a boost? That gets real complicated, real fast; @KorvinStarmast's answer does a good job of pointing out the tip of that iceberg.
1 - I really didn't want to get too much into the weeds on IRL fan-boating vs. magic fan-boating. The weird quirk being that IRL fan-forward works but is less efficient than fan-backward, whereas in magic-land the reverse is true!
At the table...
If you want to play out the chase at all, I recommend you discuss these plan with your GM ahead of time. Expecting your GM to be able to deal with windspeed differentials, point-of-sail issues, hull speeds, &c. on the fly may not yield you the chase scene you may be looking for.
Even if you don't want to game out the chase, you should give your GM a heads-up anyway. Even if you're content with a "good thinking, you get away with no trouble" your GM should have the opportuity to ponder how this will impinge upon your spell slots.
Best Answer
The web spell's effect can render some creatures entangled, a condition which can make casting spells and attacking difficult:
Emphasis mine. Otherwise, a creature's casting and attacks are unimpaired by the web spell's effect. However, creatures with the web spell's effect between them may find combat and spell targeting difficult:
Any cover prevents attacks of opportunity, for instance. And total cover blocks line of effect, which most folks need to do pretty much anything to anyone.
A quick note on the web spell's effect
The spell web does not create a lone, giant spider's web that essentially renders creatures that fail the saving throw helpless like a spider's web does its prey but creates, instead, a wall-like mass of web-like strands that creatures can try to push their way through. The effect can secure unlucky, weaker creatures in their spaces, but those creatures are still capable of exerting force and struggling against the strands—and, with difficulty, making attacks and casting spells. So while the spell says, "These strands trap those caught in them," first it says, "Web creates a many-layered mass of strong, sticky strands." How the effect traps affected creatures is governed by the condition entangled and the remainder of the spell's description.