Vitor1 - this question is really about GLM (generalized linear modeling). I'll give you a quick answer, then all the historical context you need.
Quick Answer
Yes, the direction of effects can be flipped. If we called condition 1 condition 2 by mistake, then realized it later, we could simply flip the Beta or Odds Ratio or what have you. However, in order for this to be meaningful, we would also have to take care to flip the meaning of our verbiage to reflect the truth. The same logic does NOT apply if only certain samples were flipped, but not others.
Historical Basis
Suppose you ask, "How could I learn all about this so I know exactly why the above statement is true". Here is what I would read for that:
A few hundred years ago, Gauss and Markov found that as long as certain assumptions about a dataset were met, we could guarantee that an estimate we'd make about something of interest would be guaranteed to be the best possible estimate certain ways (best linear unbiased estimate; BLUE)...
These observations today stand at the center of general linear modeling. Later on (much more recently), people realized they could still reap the benefits of BLUE even if the data were not linear, by first performing a transform, then doing the GLM, then backtransforming the data - this process of extending general linear modeling is called generalized linear modeling.
To really understand why the answer to your question is the way that it is, this is the corpus of knowledge that would need to be assimilated.
Now then, let's think about DESeq2 for just a moment. Scientists like Michael Love, in essence, used a form of GLM in order to be able to apply it to RNA-seq data. Why was this necessary? Well, because transcript quantification is based on the observation of discrete, not continuous, variables, which puts it in the category of count regression.
Nevertheless, these generalizations of the initial GLM formula obey the same rules, by and large - so they are called generalized linear models.. Specifically, DESeq2 is built on Negative Binomial regression, which is a mild adaptation of Poisson regression.
If you look at how the parameter estimates are obtained, you will readily see that the names given to them are arbitrary constructs and may be switched so long as the interpretation of said parameters is also flipped.
@Vincent gives a good answer below, but I would simply recommend avoiding the terms up-regulated or down-regulated in favor of enriched. You can think of a gene as being enriched in one condition relative to another, or maybe depleted in one condition versus another. The terms up-regulated and down-regulated imply a specific mechanism, unnecessarily. If a genes in induced in yeast by galactose, it will become enriched in that condition. But if we flip the condition, is the absence of induction the same as down-regulation? (short answer: induction and repression are complicated and genes need to be evaluated on a case by case basis). Enrichment is accurate and descriptive without implying mechanism. As @Vincent points out: "the names given to them are arbitrary constructs" - let them at least be accurate, rather than unintentionally biased.