Bootstrapped Regression Residuals This relates to using bootstrapping of residuals in regression.
I do not understand the point of this procedure, i.e. bootstrapping the errors and then adding the residual back to the predicted value. (Please correct me if I am mistaken here).
Is there some way that doing the aforementioned method would include non linearity in the otherwise linear regression model? 
 A: I'll frame this as a single-$x$ problem, since I think it covers what you need to understand.
As I understand it you're asking about an underlying situation like this:
$E(y) = g(x)$ where $g(x)$ is nonlinear in $x$.
However, you actually fit a model of the following form:
$E(y) = \beta_0+\beta_1 x$,
and apply a residual bootstrap, where you add the resampled (with replacement) residuals to the fitted values to produce a new pseudo-sample.
Because the resampled residuals are randomly assigned to fitted values, nonlinearity in the original data is necessarily destroyed in the pseudo-samples. 

Note that in the original data there are mostly positive residuals at each end and mostly negative residuals in the middle - the kind of thing you would expect if the true relationship was convex. If you resample residuals so that they're randomly assigned to observations, you won't have a cluster of positive residuals at each end and negative residuals in the middle - instead they're all over the place.
When you bootstrap residuals you rely on the correctness of the model for inference (such as confidence intervals), so if you fit the wrong model, the fit and the CIs are wrong. (On the other hand judicious use of the bootstrap may also help reveal such model inaccuracies.)
[Your question suggests you've never actually tried something like the above illustration; I highly recommend you do so. Generate not a single pseudosample but several; each should look more or less like random noise about a straight line (once in a rare while you'll discern some curving pattern but that's simply the effect of chance).]
