Actually, nobody knows. It surely depends on the particular gene in the particular physiological state of the cell (what it role of the gene[product], how is it involved in any further regulatory network, and what is the precise network topology...).
The golden way out is to invent an experimental system where you could control the expression of this gene (in a specific cell type under specific conditions) and then to analyze reaction of the cell. We do have methods to overexpress or to knock.down/knock-out genes, but as far as I know don't we have (yet) any method to precisely control the expression level of a gene.
So, eventually, there is no way to get your question answered. Only future experience will show if this does have any impact.
Biological significance and statistical significance do not need to coincide nor correlate, but they can.
You would be better served assessing the situation as a wider phenomenon: can you also measure the change in protein levels of the relevant genes? Are they genes that are highly expressed anyway, or genes that usually are maintained at very low level? What biochemical role do they play, and is this a role that lends itself to modulation over such a narrow expression range?
For instance, a 20% increase in expression of a myosin heavy chain gene would be a comparatively mild effect when assessed as fold-change, but a massively relevant change physiologically, since MHC genes are high-expression and fairly stable. Conversely, a 20% increase in expression of MyoD would be far more likely to represent biological noise, since MyoD is a transcription factor that undergoes 10-fold expression changes during myogenesis.
Apologies for the muscle-centric answer, but basically: this is something you should determine on a case-by-case basis. And as Jochen neatly summarises, there may be no good answer.