X on the off chance Y
Indicates that some action (described by a complete clause X) is undertaken in hopes that it brings about (but probably will not) another action (described by complement clause Y).
Y (which is required) must be a complement clause introduced by that (that could be omitted in informal styles, but keep it in for a research paper). A model usage would be:
David took the 7:30 train home on the off chance that he would see Mira.
Furthermore, Y usually has a modal auxiliary as its finite verb (could, would, might, should).
To reword your sample sentence so that it fits the template for this expression,
The main disadvantage of these approaches is that they tend to be undertaken on the off chance that they could succeed, rather than with definite expectations about when they will bear fruit.
A commenter has correctly pointed out that Y could also be a gerundive verb phrase introduced by the preposition of (e.g., "of succeeding", "of finding a way out of the cave"), as in
David took the 7:30 train home on the off chance of seeing Mira.
A slight variant of the construction is a type of conditional construction:
(If) On the off chance Y, X.
Which indicates some action represented by X that should be taken in the (unlikely) event that Y occurs. Here, Y usually does not have as its finite verb a modal auxiliary. e.g.,
(If) On the off chance that you see butter at the store, buy two pounds.