There certainly is such a gradient, but what it may be depends on the gearing of your bike. Humans are very low-geared mechanisms and there comes a point where you would have to reduce the gearing  of your bike to a 1:1 ratio. At that point a bike is just an extra weight to lug uphill. Also, your sense of balance had better be better than mine, because you would have a lot of trouble staying erect as such a low speed.

If you find a trike with suction wheels though, and you could reduce the gear ratio to well under  1:1, and you could put up with pumping away several times for each step, and you had a ratchet to prevent your rolling backwards, then you could go (slowly) up a vertical slope, which would be quite tiring on foot.

cycling is quite efficient, both as a muscular action as mechanically - as above, a 1:1 gear ratio offers no mechanical advantage over walking, but you'll still generally be slightly quicker than walking (even if you walked up without the extra weight of the bike).

The problems are balance - both going fast enough for lateral balance, as above, and vertical balance.  If your effective centre of mass moves outside of the tyres, laterally or vertically, you'll fall off.  The force required to stop you rolling down the hill are applied at the rear tyre at ground level, creating a moment that threatens to rotate you - this can be seen on level ground by pedalling hard in the saddle in a very low gear - 1:1 will normally be low enough - as you experience a wheelie.  You can move your bodyweight forward to stop this, but too far and the rear wheel will spin.  The steeper the hill, the narrower the balance point becomes - on a vertical slope, the rear wheel would either fail to deliver any force at all, or flip you over backwards, so climbing a vertical slope without special gear is definitely out!