The error when you attempt to use the Debian 8 instructions suggests lots of missing dependencies, but in fact will work if you install the single actual missing dependency (libssl1.0.0). For reference, to work out what was missing, I downloaded the mongod binary and had a look at ldd:
adam@debian9:~/mongo/mongodb-linux-x86_64-debian81-3.4.6/bin$ ldd mongod
linux-vdso.so.1 (0x00007ffd0e15d000)
libssl.so.1.0.0 => not found
libcrypto.so.1.0.0 => not found
librt.so.1 => /lib/x86_64-linux-gnu/librt.so.1 (0x00007f93c6dff000)
*snip*
If you have a look at what is installed in Debian 9, basically we just have versions of libssl that are too new. The libssl and libcrypto libraries are both installed by the libssl package and it is pretty much standalone. Hence, we can just grab the Debian 8 libssl1.0.0 package and install that.
The amd64 version of the package can be found here (just Google for libssl1.0.0 Jesse and your arch for another version).
To install that package, download the file (in my case it was to Downloads) and then install it with dpkg:
adam@debian9:~$ sudo dpkg -i /home/adam/Downloads/libssl1.0.0_1.0.1t-1+deb8u6_amd64.deb
Selecting previously unselected package libssl1.0.0:amd64.
(Reading database ... 126471 files and directories currently installed.)
Preparing to unpack .../libssl1.0.0_1.0.1t-1+deb8u6_amd64.deb ...
Unpacking libssl1.0.0:amd64 (1.0.1t-1+deb8u6) ...
Setting up libssl1.0.0:amd64 (1.0.1t-1+deb8u6) ...
With that complete we quickly re-check ldd:
adam@debian9:~/mongo/mongodb-linux-x86_64-debian81-3.4.6/bin$ ldd mongod
linux-vdso.so.1 (0x00007ffdf25de000)
libssl.so.1.0.0 => /usr/lib/x86_64-linux-gnu/libssl.so.1.0.0 (0x00007f86bc12d000)
libcrypto.so.1.0.0 => /usr/lib/x86_64-linux-gnu/libcrypto.so.1.0.0 (0x00007f86bbd31000)
librt.so.1 => /lib/x86_64-linux-gnu/librt.so.1 (0x00007f86bbb29000)
*snip*
Success! Now let's retry the package installation of mongodb-org:
adam@debian9:~$ sudo apt install mongodb-org
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following additional packages will be installed:
mongodb-org-mongos mongodb-org-server mongodb-org-shell mongodb-org-tools
The following NEW packages will be installed:
mongodb-org mongodb-org-mongos mongodb-org-server mongodb-org-shell mongodb-org-tools
0 upgraded, 5 newly installed, 0 to remove and 0 not upgraded.
Need to get 66.8 MB of archives.
After this operation, 270 MB of additional disk space will be used.
Do you want to continue? [Y/n]
Get:1 http://repo.mongodb.org/apt/debian jessie/mongodb-org/3.4/main amd64 mongodb-org-shell amd64 3.4.6 [7,980 kB]
Get:2 http://repo.mongodb.org/apt/debian jessie/mongodb-org/3.4/main amd64 mongodb-org-server amd64 3.4.6 [14.2 MB]
Get:3 http://repo.mongodb.org/apt/debian jessie/mongodb-org/3.4/main amd64 mongodb-org-mongos amd64 3.4.6 [8,103 kB]
Get:4 http://repo.mongodb.org/apt/debian jessie/mongodb-org/3.4/main amd64 mongodb-org-tools amd64 3.4.6 [36.5 MB]
Get:5 http://repo.mongodb.org/apt/debian jessie/mongodb-org/3.4/main amd64 mongodb-org amd64 3.4.6 [3,820 B]
Fetched 66.8 MB in 7s (9,509 kB/s)
Selecting previously unselected package mongodb-org-shell.
(Reading database ... 126491 files and directories currently installed.)
Preparing to unpack .../mongodb-org-shell_3.4.6_amd64.deb ...
Unpacking mongodb-org-shell (3.4.6) ...
Selecting previously unselected package mongodb-org-server.
Preparing to unpack .../mongodb-org-server_3.4.6_amd64.deb ...
Unpacking mongodb-org-server (3.4.6) ...
*snip*
Adding system user `mongodb' (UID 119) ...
Adding new user `mongodb' (UID 119) with group `nogroup' ...
Not creating home directory `/home/mongodb'.
Adding group `mongodb' (GID 123) ...
Done.
Adding user `mongodb' to group `mongodb' ...
Adding user mongodb to group mongodb
Done.
Setting up mongodb-org (3.4.6) ...
Finally, let's make sure the service starts and we can connect with a shell:
adam@debian9:~$ sudo systemctl start mongod
adam@debian9:~$ mongo
MongoDB shell version v3.4.6
connecting to: mongodb://127.0.0.1:27017
MongoDB server version: 3.4.6
And there you have it - Jesse packages working on Stretch. I'm sure that there will be an official release soon that will make this obsolete, but in the meantime this is a relatively painless workaround.