It depends on the size of the inserts relative to the reads length. As explained by genomax2, if the read length is greater than the insert length, you will sequence through the insert into the adapter on the other side of the insert.

At our molecular biology platform, our median fragment size, before adding the adapters is 150 bases. Our read length is 50 bases. Since we never sequence into the adapter on the other side of the insert, trimming is useless. It is not detrimental to perform it on our samples, just a waste of computational resources.

You could check with the technicians who prepared the libraries the size of the fragments before the adapters were added. If you cannot obtain this information, you needn't worry. You can just use FastQC to check for the presence of adapters. You can also estimate the distribution of fragment lengths after alignment with Picard tools. To remove the adapters, you can just run Trimmomatic in paired end mode. Trimmomatic already comes with the adapter sequences.

You should first run FastQC on your samples, which will give you useful quality control information anyway. Then you can run Trimmomatic. If the quality of the bases is good, and there are no adapter sequences present, running Trimmomatic will not improve your alignment results, but will not have too much of a detrimental impact either. If there are adapter sequences present, or many low quality bases, your alignments results will be improved after trimming.

The reads need to be trimmed. -m is the distance for setting. you need set -r/--mate-inner-dist parameter when you want to do Tophat.