If I select any two tips randomly, without a full knowledge of the tangle, will it change the probability that my transaction will be selected by other transactions?
Selecting 2 random tips will impact negatively the probability for your transaction to be confirmed by others. There are multiple reasons for that:
There is a chance that 2 randomly selected tips are inconsistent. (i.e. your transaction would approve a double spend and will never be selected by any other transactions selected by the recommended GTTA algorithm). This situation is impossible with the recommended GTTA.
There is a chance that one of the randomly selected tip is not solid and will never be solid because one of it's branch or trunk simply don't exists. Therefore your transaction will never be solid and will never be approved by anyone else. This situation is impossible with the recommended GTTA.
Most importantly, the recommended GTTA algorithm is more likely to select tips to approve in the main tangle branch. If you select 2 tips completely randomly: the probability that they are in the main branch is lower than with the recommended GTTA algorithm. As a direct consequence : the probability for your transaction to be approved by others decrease.
I think those 3 points are relatively simple to understand and should give you the intuition that selecting 2 tips completely randomly will never increase your probability to be confirmed.
How much does it decrease is a more complex problem and the most efficient way to estimate this is probably by running simulations/real world measurement.
As a side note researchers from the IF already run tangle simulations and published the results, not directly answering your question, but at least giving you an idea of how the random walk parameters impact the probability to be confirmed.
Related links :
Alpha: playing with randomness (for an explanation of the random walk and how it can be fine tuned)
Confirmation rates in the Tangle (presenting the results of various simulations)