Our current genomic sequencing technologies have one key shortcoming that could be exploited in order to hide a genomic sequence. Most current whole genome sequencing technologies rely on a technique called “shotgun sequencing”. This involves fragmenting the chromosomes into many small pieces hundreds of base pairs in size. Hundreds of millions of these fragments are then sequenced simultaneously to produce “reads”. These reads are then fed into software which attempts to piece the genome back together. This shotgun sequencing strategy works very well, except in one particular case. Wherever you have long stretches of repetitive elements the strategy fails. This is because there is no way to use the short reads to determine how many repeats are in the repetitive elements. Even when the reads aren’t perfectly repetitive the issues of infrequent sequencing errors preclude the possibility of anything other than a probabilistic model. The result of this shortcoming is that the human genome (and every other genome we have sequenced) has large unassembled gaps. These are repetitive sequences where we know the beginning and the end and roughly the size of them and roughly what the repeats are inside them, but can’t actually put all the pieces into place. In humans the largest of these are the centromeres which are generally millions of base pairs in size. So, there exist huge gaps in our current genome assemblies that could be used to hide genomic sequences.
Sounds great on paper right? But there are a few issues with this idea. The first is that if you try to hide a viral element inside an otherwise repetitive region you only obscure its precise location, not its existence. The sequence you’ve inserted will still be sequenced by shotgun sequencing techniques, and since it isn’t repetitive it will be assembled. If it’s flanked by repetitive sequences the scientists won’t be able to know exactly where it is in the genome, but they will know it is in the genome. This means your sequence still needs a disguise. The flanking repetitive elements will disguise the fact that your insertion is a novel change to the genome since we don’t know what was there before, but if the sequence looks like an artificial virus it will be discovered if people look for it. Other answers and comments have some good suggestions here. Endogenous retroviruses account for ~9% of the human genome and some are believed to still be active. Making the insertion appear to be contamination from a bacterial source also has some potential. As does using intronic segments to split up the viral gene into multiple pieces, ideally separated by repetitive sequences matching the insertions surroundings.
Another potential issue is position-effect variegation. Repetitive elements tend to be epigenetically silenced so that they won’t be transcribed. That said there are multiple instances of genes within repetitive pericentromeric regions that are still transcribed. Just mentioning it as an additional hurdle to overcome.
Another shortcoming is that this approach is reliant on our current shotgun sequencing technology. Newer sequencing technologies like single molecule real time sequencing are still much more expensive than shotgun sequencing, but have the potential to close up these repetitive gaps due to longer read lengths. Within the next few decades, if sequencing technologies continue to advance it is unlikely there will be anywhere to hide.
Finally, if scientists are really actively searching for this virus I don’t see how they wouldn’t find it. You’ll never be able to disguise it perfectly and have it still be functional. Even something rudimentary like taking all of the human sequencing data produced before the virus entered the population and comparing it to all of the sequencing data produced afterwards will detect any additions in the population without even having to worry about assembling the data. If you truly want to make a change that is undetectable you have to work within the confines of existing human variation.