I'm not sure, but I think there may be a difference in meaning of "score" in the above discussion. "Score" to most people means the points earned by merging blocks, whereas Isaac appears to be using the word to mean the maximum value shown on a single block. I will use the majority definition. And I apologize for not having quick and handy access to all the symbols and superscripts; please bear with me.
To answer Saryu first, yes, for the standard game (Isaac's game uses only 2's, so 2^16 is the maximum block value for his game). 2^17 is reachable if and only if a 4-block appears instead of a 2-block when the board reaches its maximum state for the 2^16 pattern, thus allowing another series of merges to occur.
Unfortunately, I can't offer a rigorous proof, but I can offer my numbers and let you folks make of them what you will. I will primarily discuss the standard game, of which Isaac's variant could be considered a subset as it does not include 4-blocks.
The block values on a maximum board (m = n^2 = 16) are established as 2^(m+1), 2^m, 2^(m-1)...2^3, b (either a 2 or 4).
The maximum score value of a given block valued 2^k, according to my reasoning, is (2^k)(k-1). Since either I'm misreading Flowers's formula or I've reached a different conclusion, I reason as follows: since score is gained each time blocks are merged, the maximum number of merges to create a block of 2^k would be done with blocks of size 2, and would be 2k-1. To derive score, imagine a line of 2-blocks long enough to add up to the desired 2^k value, and then take them through successive pair-merges (merging each pair of adjacent blocks throughout the line in a single operation) until you end up with the single block of 2^k. Each of these pair-merges would score 2^k points. The number of pair-merges required would be (k-1).
A brief example to illustrate k=3: a line of 2222 is pair-merged to 44 (each 4 scoring 4 points, total 8), and then pair-merged again to 8 (scoring 8 points). Each pair-merge was worth 2^k points, and k-1 of them occurred, thus (2^k)(k-1) for the total score value of 16.
Since in the real game merges may only occur of equal blocks, and since each 2^k value must be built up by successive merges, I cannot find any logical reason why this method does not derive the maximum possible score value for a given 2^k block. However, since 4-blocks sometimes appear in the game, the actual score obtained may be lower...in fact, it will be 4 points lower for each 4-block which appears, since no points will be obtained for the creation of that 4-block from a pair of 2-blocks. If my reasoning thus far is correct, the maximum score value for the official game's maximum block size (k=17) is thus 2097152. For Isaac's variant (k=16) it would be 983040.
From that basis for maximum possible score of a single block, and knowing the maximum board position, we can then sum the maximum scores of each block on that board to obtain a maximum possible score for the entire board. I admit that at this point I "cheated" and used Excel to do totals and then deduced the formula therefrom, but I think the conclusions are still valid.
For Isaac's version, the sum for k=2...m of (2^k)(k-1) equals (2^k)(2k-4)+4, or 1835012.
For a standard board, the sum for k=3...m+1 of (2^k)(k-1) equals (2^k)(2k-4). This is 3932160, which I assure you is a far higher score than I've ever obtained. However, this sum neglects the fact that for the k=17 block to occur, a 4-block must (as stated earlier) have appeared at a particular point, and since each 4-block reduces the score by 4 points, the actual value is (2^k)(2k-4)-4, or 3932156. Which is still a lot higher than I'm ever going to score...