An upper bound for the most plants an optimal solution can have is 62.
64 plants is impossible
A solution with an odd number of plants 2n+1 or an even number of plants 2n must contain at least n empty spaces in order for all those plants to be reachable. (Put another way, if we have n empty spaces, all connected by other empty spaces to the entrance, the most plants we can reach is 2n+1.)
So if a solution with 64 plants exists, that solution must contain at least 32 empty spaces. Thus, such a solution must contain at most 3 sprinklers.
If 3 sprinklers are to water 64 plants, at least one of those sprinklers must water at least 21 plants*. However, any arrangement of 21 (or more) plants around a sprinkler must contain plants that are not reachable, even if we assume the arrangement is surrounded by reachable empty spaces**. Thus, no solution can have a sprinkler watering at least 21 plants, so a solution with 64 plants is impossible.
That any solution with more than 64 plants is also impossible is trivial.
63 plants is impossible
By our logic so far, a solution with 63 plants would require at least 31 empty spaces.
The 2n+1 maximum number of reachable plants can only be obtained if the n empty spaces form a straight line up from the entrance. But a 31-space straight line would not fit in our 9x11 greenhouse. In order to fit 31 connected empty spaces into the greenhouse, there must be some 'wasted potential': for example, for every "corner"
that exists in our set, we can deduct 1 from the maximum number of plants the arrangement can reach. (T-junctions, crossroads, and four-squares are even more wasteful.)
I freely admit this is somewhat woolly, but my contention is that fitting 31 (or more) connected empty spaces into a 9x11 grid requires at least three points of wastage. (Note that, for instance, the longest possible path with only two corners contains 11+8+10 = 29 spaces, and this is ignoring the fact that path is highly suboptimal because of the greenhouse's edge.)
Thus, for n 31 or greater, the maximum number of reachable plants is 2n+1-3 = 2n-2, and so a 63 plant solution would require at least 33 empty spaces. This leaves at most 3 spaces for sprinklers, so once again we require at least 1 sprinkler to water 21 plants and we reach an impossibility.
Even this upper bound is quite loose: it underestimates the amount of wastage there will be, it doesn't account for empty spaces at the edge of the greenhouse not reaching new plants outside the greenhouse, and it doesn't account for the fact sprinkler blocks need to fit into the greenhouse and be reachable through/around each other.
*In fact, 22, but 21 saves time later
**Such a 5x5 block would contain 1 sprinkler (at its centre), 21 plants, and 3 empty spaces. An empty space on the exterior ring of the block will make at most 1 extra plant on the interior ring reachable. An empty space on the interior ring of the block will make at most 2 extra plants on the interior ring reachable. Since there must be at least 1 empty space on the exterior ring of the block in order for any of the interior ring of plants to be reachable, there are at least 6 plants on the interior ring of the block, and thus there is no way of making them all reachable.