"Diddling" can be broken down further
Which leads to the answer "it's mostly possible but be careful and do your research please"
Note: From here on out, I'm going to assume you're talking about species that reproduce sexually. If you're describing asexual
reproduction, there is no need or even want for the other party to have sex in most circumstances - therefore,
the answer would probably be no.
As other answers have pointed out, there is a community for virtually any sexual interest. Assuming your alien species is the same way, there are likely to be some pairings, though unconventional. Attraction can happen.
It's worth noting that some species do not have consensual sex, even on Earth. It is possible (although unlikely) that this alien species reproduces this way. Therefore, it's possible that one party involved in this exchange (human-alien) may not ever give consent.
By the time we observe aliens, we will likely have the technology capable of translating their language. Sound waves? Great, we can speak those. Light? Can be recorded and reproduced. Tactile communication? As long as they aren't toxic, sure. This is important if you want consensual pairings.
Assuming sex "feels good" for your alien species, as it does for many animals on Earth, then there must be something that can be stimulated to do so. Perhaps a human would need a machine to produce those effects - ex. light, magnetism, electricity, extreme heat or cold - or perhaps it would be tactile, something humans can mostly accomplish.
If sex does not feel like anything for your aliens (or the gender involved with humans does not usually give consent) then the motivation behind sex, assuming still that there is consent when a human is involved, could be for profits. That eliminates the stimulation problem.
Reproduction? Statistically impossible
First and foremost, these organisms are probably very different from us genetically. Major differences in genetic code, and in chromosome count, make it so that cross-species reproduction will not work (most of the time) on Earth. If your aliens have a completely different LUCA (last universal common ancestor) there's no telling how different these things will be!
Additionally, there are many speculative replacements for DNA out there - numerous molecules can carry "genetic" information effectively. It might not be a question of different genes or a different chromosome count, but rather XNA instead of DNA.
It's also worth noting that reproduction requires compatible gametes - sperm with eggs, etc. There are other effective ways to make this transfer - alien gametes may not be able to interract with human gametes.
Finally, the idea of cross-species reproduction also assumes that males are diddling with "female" equivalents, and that females are diddling with "male" equivalents. (1) Even if genes and chromosomes are compatible, DNA is present, and gametes are compatible, perhaps the ones that give birth are the "males" - like seahorses - and the females transfer the genes to them. Acts with this species would result in combining sperm with sperm, or eggs with eggs. (2) It's the future; ideas become more liberal as time passes. How many of these acts will be "heterosexual"?
Healthy timeframe? It depends
Metabolisms vary between organisms. Humans are born, see the world, live, and die through generations while single generations of some trees are around. Millions of successive generations of bacteria flourish throughout a human lifespan.
If your aliens have similar metabolisms to us, expect somewhat healthy timespans. If they have longer or shorter - expect complications.
Safe? It depends
See my answer to this question, which addresses the possible effects of alien organisms on Earth crops. The same ideas apply:
There is no reason for diseases to be compatible if they evolve different genetic material, but the toxins they release may harm humans - and vice-versa. Or perhaps the aliens themselves are toxic to humans! It all depends.