Yes and no. Most nascent (newly made) mRNAs are delivered into the cytoplasm of the cell (where protein synthesis occurs) and are translated when docked with the ribosome, but many are not free-floating. This is especially true in eggs and early embryos, where many mRNAs are specifically localized to certain areas by binding proteins or by tethering to the cytoskeleton.

In bacteria (no nuclear compartment), mRNA is often translated (loaded onto ribosomes) as it is being transcribed from the DNA, and thus is never freely diffusing. And even in bacteria, certain mRNAs may be localized to specific regions of the cell by these targeting/tethering mechanisms. In this way, the cell can regulate when and where the protein gets made "post-transcriptionally."

In regard to tRNAs, the aminoacyl tRNA is literally delivered to the ribosome by an elongation factor called Tu (EF-Tu) in bacteria and EF1alpha in eukaryotes, which takes that aa-tRNA right to the ribosomal "A site" as soon as it is made by the synthetase. Why? The simplest explanation is efficiency. It turns out that the activated ester bond of aa-tRNA is quite labile -- if left to diffuse, it would be hydrolyzed by water before it reached the ribosome. EF-Tu protects this bond from hydrolysis and helps "target" the aa-tRNA to the proper site on the ribosome.