Yes you can align sequences manually using a manual sequence alignment software of your choice, or what is more common is to use an alignment algorithm (muscle, clustalo) and then check/ adjust this in the manual sequence aligner.
Are you asking whether it is possible to manually align ITS sequences or are you asking if it is possible to request an alignment from an author? Either case the answer is yes. If you are talking about manual alignment then Tyler did a good job explaining this. If asking about asking an author for an alignment then you just need to email them or reach out on ResearchGate.
Often when an author says the sequences were manually aligned they usually meant that the put their sequences through an aligning algorithm (clustal, muscle, etc.) and then reviewed the alignment and manually made changes in areas where the aligner did not preform well, like areas where insertions/deletion are common. This is often the case for certain loci like ITS1, ITS2, and SSU. For example almost every paper using SSU will say that they manually aligned the sequences and removed the less conservative regions where alignment is questionable from their analyses. For SSU it is not enough to just toss the sequences in an aligner and just go with what the program gives you, you need to review the alignment and probably make manual changes. Also for some loci manually alignment just means that they were put into an alignment and no changes were made. For example I have had to say the sequences for ATPase 6/8 were manually aligned, however they all started with the same start codon and ended with the same end codon and were the same length since it is coding. In this case putting sequences into an aligner algorithm would be a waste of time since the sequences are already aligned.
So, manually alignment does not necessarily mean least accurate, in some cases it may be more, in some it may be less, and in others it does not make a difference. This is why most author have to say that the alignment is available upon request or make the alignment available on databases like TreeBase so that others can review them and make their own judgement.
Hope this helps, and I wish the answer was a little more cut and dry, but alignments can be tricky at times.