I would certainly plan for the expectation of being walked out once you give notice. Many places have those kinds of policies, and for good reason--apart from paranoid concerns about stealing information, sabotage, etc., it can be very de-motivating to the team to have someone still there but talking about their exit plans.
I have personal experience with this--I got an offer for a competing company with a flexible start date, and didn't want to leave my current project in the lurch. So I gave notice but said if you want me to keep working another couple of months that would be fine. At first, my supervisor and management above that was very appreciative, since I was in the middle of a bunch of work and it would have been disruptive to have me just suddenly depart. They accepted my offer to stay on while they found a replacement. Then the next day they came back and said we only want you to finish this list of critical tasks, and you will be done in 2 weeks. Then the next day they came back and said you're done, off the project as of today, and gave me a final 2 weeks of pay without even working.
At the time I thought it was all handled very unprofessionally--I was trying to do the honorable thing, and felt very insulted by the way they handled it. Looking back on it though, word spread about my impending departure quickly, and people were asking me at lunch, etc. about my new role at the competing company. I expect that's why I was eventually suddenly removed.
This might be more common in larger corporate cultures--if you work for a small or mid size company and you have relationships with the owners/top executives personally, then it may not happen that way. I would just advise that you go in prepared for that outcome once you give notice, and try not to be surprised or insulted if they ask you to leave immediately.
Back to your main point though, there's no harm in offering a more gradual transition, and in your shoes that's probably what I'd do, once I had "enough" and could handle the above outcome. I think it's a fine and honorable thing to do, treating them the way you'd like to be treated.
If you're leaving to stop working as you seem to be replying, one idea might be talking about retiring or taking a "sabbatical" rather than quitting, as those kinds of departures are more typically planned in advance, and might not trigger the same "policy" as someone quitting to start a similar job elsewhere.